Poprad, Slovakia

Take one small city with a heart of medieval mitteleuropean quaintness at the foot of magnificent, snowy mountains. Then add an open-air spa where everyone has year-round fun, be it quietly relaxing in hot pools or screaming down water slides. The happy result is Poprad in Slovakia. Its historic centre, Spišská Sobota, is not huge, but its baroque architecture places it firmly in an old and very central part of Europe. Vino and Tapas on leafy Sobostské Square does great-value fine dining; for accommodation, Pension Sabato (doubles from €60 B&B) has a lovely garden at the back.

Be sure to venture beyond the old town to discover the highlights of other districts, notably chocolatier Bon Bon on Dominika Tatarku, over the river near the station, and the Podtatranské historical museum on Partizánska Street further west. Best of all is the quick, cheap public transport to the High Tatra mountains, with cable car connections for skiing or just enjoying spectacular panoramas. Starý Smokovec is the main village. Back in town, the spa, Aquacity, is hugely popular with locals (family day ticket €52). Those whose idea of enjoying cold weather is a long lounge in an open-air hot pool before breakfast can even stay here (doubles from €119, including spa access).
• Wizz Air flies to Poprad from Luton from £44 return

Baden-Baden, Germany

So good they named it twice? Actually the double title is to distinguish it from all the other Badens around Europe – the name just means “to bathe”. Nevertheless this spa town has venerable traditions of immersion, and celebrity visitors ranging from the Roman emperor Caracalla to Queen Victoria and Victoria Beckham and the England Wags at the 2006 World Cup. In the 19th century, when fragile health was a life’s work for the idle rich, the place was packed with aristocrats drawn by the promise of salvation in the waters, and diversion in the casino. (Fyodor Dostoyevsky lost a small fortune there in 1867.)

The town remains perfectly set up for easygoing entertainment and is lovely in winter, with the warm waters great for easing chilly bones. Lichtentaler Allee is a lovely landscaped ribbon of gardens that threads its way across town; visitors can sip the allegedly curative waters in the Trinkhalle, or just sink into them at Friedrichsbad Roman-Irish Baths (basic three-hour experience €25). Mark Twain said he lost track of time in 10 minutes and the entire world in 20. (He also said Baden was an inane town, “filled with sham, and petty fraud, and snobbery” - which seems harsh when he also claimed it cured his rheumatism.)

There are plenty of upmarket restaurants offering specialities such as beef cheeks in pinot noir. Osteria Stromboli is a decent budget alternative, with homemade pasta from €6.90. Café Konig on Lichtentaler Strasse is where Leo Tolstoy drank coffee 20 years before he recycled his Baden-Baden experience in Anna Karenina. For budget stays, the youth hostel north of town has dorm beds from €21.80. Otherwise the central Hotel Etol (doubles from €110 B&B) is a reliable bet. In winter, or in fact in any season, the nearby Black Forest national park has lots of activities to offer, including trekking, but also a classic drive along the Schwarzwald Hochstrasse, route 500.
• Ryanair flies from Stansted to Baden-Baden from £30 return

Sarajevo, Bosnia

In this cruel world, Sarajevo is a reminder that bad things can turn out better. This once magnificent bastion of integration and multicultural splendour has risen from the ashes of the 1992-96 siege and is now a flourishing metropolis and fascinating destination. Narrow alleyways in Baščaršija, the old town, are packed with good cafes and decent well-priced accommodation. Hostels such as Balkan Han, The Doctor’s House and Franz Ferdinand have dorm beds from €11, doubles from €32.

Highlights are the restored town hall, a masterpiece of fin de siècle Moorish fantasy, plus Svrzo’s House, a dignified museum recalling the atmosphere of 18th-century Sarajevo. More up-to-date, and no less evocative, is the Tunnel Museum, a section of the passageway that kept the city alive during the dark days of the war. For dinner, Cakum-pakum is something of a legend for its homeliness and well-priced stuffed pancakes. As befits a Winter Olympics location, there’s skiing and snowboarding in Bjelašnica, 20 miles to the south-west. Jahorina to the south-east is good for off-piste action.
• Eurowings flies from Stansted and Heathrow from £140 return

Åre-Östersund, Sweden

Bayeux is not the only place for 900-year-old tapestries; the Överhogdal Tapestries, now housed in the northern Swedish town of Östersund, were rediscovered in a church about a century ago. These Viking weavings at the Jamtli Musuem, (free entry) reveal, in extraordinary detail, a world that was just beginning to adopt Christianity. Not that Östersund is lacking in modern attractions: it also has contemporary art galleries, and the ski centre of Åre, Sweden’s only world-class downhill slopes, is nearby. If skiing isn’t your thing, there are loads of family-friendly activities in the Winter Park: ice-sculpting sessions, skating, sledging or lying back in a deck chair sipping hot chocolate.

For snacks and cakes, locals head to Wedemarks or Törners bakeries, both in the small pedestrianised centre; for more serious dining, Fäviken, one of the world’s great – and remotest –restaurants, is 50 miles away, deep in the wilds. Here chef Magnus Nilsson has made rustic Scandinavian cuisine into an unlikely success story. There are rooms at Fäviken (£215 B&B) for those happy to book months in advance, but closer to town (eight miles away) and great value is Sorbygarden B&B (doubles from £69 B&B). Cosy Hotel Emma (doubles from £75 B&B) is a more central alternative. Skiers could try Hotel Åregarden in the centre of Åre (doubles from £119). A new easyJet flight from (11 December) makes the area more easily accessible from the UK – apologies to those Stockholmers who used to keep it as a secret winter bolthole.
• EasyJet flies from Gatwick to Åre-Östersund from £72 return

Poznan, Poland

Bombed to bits in the second world war but rebuilt and rejuvenated, Poznan is an energetic student town with great bars and cafes for cosying up on chilly winter days. The heart of it is Stary Rynek, the old market square, surrounded by colourful merchants’ houses now mostly devoted to eating and drinking. The best cafes, however, are a short walk away from the main tourist drag: Piece of Cake (Zydowska 29) does excellent coffee too, and Brisman (Mickiewicza 20) is a brilliant little bar decorated with Star Wars memorabilia. For dinner, Ratuszova (mains from £7) is right in the centre and good for Polish specialities.

Those on a budget could just fill up from delis and patisseries: Poznan does several special cakes, most famously the St Martin’s croissant (rogale marcińskie), an 81-layer concoction that is a meal in itself. Staying with the patisserie theme, the town hall which dates back to the 13th century looks like a wedding cake crossed with a lighthouse. It was here that Heinrich Himmler’s infamous Posen speeches were recorded in 1943, revealing Nazi plans for the “final solution”. Today, the building is a museum and the clock outside is the big attraction: every day at noon a herd of mechanical goats appear and stage a battle.

For accommodation, Hotel Puro (doubles from £70) is smart and central with a retro feel. A good budget choice is the Very Berry Hostel up the road (dorm beds from £6, doubles from £15, breakfast £2). Winter visitors can escape the cold for a while in the huge tropical greenhouse at the city’s botanical garden, Wilson Park.
• Wizzair flies to Poznan from Luton and Glasgow from £52 return; Ryanair flies from Stansted, Bristol, Liverpool and Edinburgh from £35 return

Zagreb, Croatia

One of Europe’s youngest capitals, Zagreb is also one of the most fascinating, with attractions including the extensive Hrelić flea market, plus musuems covering everything from archaeology to broken relationships. The quirkiness extends to the food – try prosciutto-wrapped frogs (£11) at Didov San, or eggs in chilli sauce at Mundoaka. For traditional Croatian dining, the homely Tač (restac.hr) on a nondescript suburban street is hard to beat. Drinking coffee is something that Zagreb specialises in: Café u Dvoristu (Jurja Žerjavića 7/2) and Finjak (Vlaška 78) are both popular with locals. Tkalčićeva Street is the busiest for bars and restaurants: don’t miss štrukli, sour cream and cheese-stuffed pastry that can come either baked or boiled.

There are plenty of decent hostels, but those after a bit more style will enjoy Art Hotel Like (doubles from £60). In winter, Zagreb comes alive: Zrinjevac park teems with Christmas decorations and, it seems, half the city’s population. There’s an ice rink at the railway station and unusual Christmas shopping on Tomićeva and Bogovićeva streets. Zagreb has good connections to Sljeme, for skiing or snowboarding right next door to the city. To just drink in mountain scenery, take a bus to the lovely village of Samobor.
• British Airways flies from Heathrow from £100 return

Tromsø, Norway

Want to see the northern lights? My hot tip is to live in hope, but expect nothing. The best chances are had in northerly destinations away from the coast. Tromsø fits the former category nicely: it’s about as far north as you can get in mainland Europe on a budget airline. It lies on an island in a fjord, so is not exactly inland, but almost. The city has plenty to entertain those waiting for the aurora: good cafes – try Aunegården (Sjøgata 29) or Riso mat & kaffebar (Strandgata 32) – and a couple of interesting museums (war in the Forsvarsmuseum, and the Arctic and Antarctic in the Polarmuseet). For dinner, a 26 bus then a cable car up Mount Storsteinen (fjellheisen.no) with its cafe and restaurant offers a great view (and possibly some aurora).

In town, young people hang out on reindeer hides on the terrace of the Raketten kiosk on Erling Bangsunds Plass, where the hot dogs are excellent. Another small but fun spot is Huken Pub, which does burgers and jacket spuds of generous proportions. There are plenty of warm efficient hotels, but for a bit more character try the self-explanatory Bed&Books guesthouse (doubles from £90, bedandbooks.no) A trip into the wilds is easily arranged: there is whale-watching in the fjord right into February some years, plus dog-sledding, skiing and, for those who wish, coach trips that chase the northern lights.
• Norwegian flies from Gatwick from £190 return, or via Oslo from Manchester

Ljubljana, Slovenia

The former home of president-elect Trump’s current wife, Ljubljana is a lively place – 50,000 students ensure that – and very green (it is the 2016 European Green Capital), with traffic restrictions leaving the banks of the Ljubljanica river a great strolling and cafe zone. There is some impressive architecture: the medieval castle, the baroque Robba fountain, a slew of great bridges, and many contemporary jewels. With all those students there is, of course, plenty of good coffee: Čokl (Krekov 8) is a tiny spot near the funicular railway, and Daktari next door puts on live events in what feels like a much-loved living room.

Self-caterers can stock up at the market on Pogačarjev trg (Wednesdays and Sundays) and check out the nearby covered market for cheeses. In winter, cafes offer mulled wine as well as the dry whites in which Slovenia excels, and there is a good Christmas market. Among the better restaurants are the atmospheric Taverna Tatjana and Špajza. Horse fillet (from €12) is a favourite at both.

The Adora Hotel (doubles from €64) a short walk from the old town, is stylishly comfortable, with lots of polished wood reflecting the grey and lime green colour palette. The city is a good base for day trips to ski areas such as Krvavec, 15 miles away. The Sava river, north of the city centre, is great for water sports, including canoe slalom at the Tacen world championship course.
• Wizzair (Luton) and easyJet (Gatwick and Stansted) fly to Ljubljana. Prices from £30 return

Memmingen, Germany

This undiscovered gem in deepest Bavaria has guarded its architectural treasure through several cataclysmic wars – one of the town’s tower, the Lindauer, boasts an embedded cannonball from 1647. It would make a great location for a Chitty Chitty Bang Bang remake (God help us!), with quirky splendours aplenty in the restored brothel (the Frauenhaus), the splendid seven-roofed tannery (Siebendächerhaus) and the Fishertag fountain, site of an annual festival in July that sees young men jumping into a little river to catch trout.

Cycling is popular in summer: cycle hire at the airport links to an enviable network of trails. In winter, feet may be more reliable, taking in the fine Salzstrasse and Weinmarkt before finishing on Schrannenplatz at Zum Goldenen Löwen, the city’s oldest tavern, built in 1590. Also worth seeking out is Cafe Kunz, for its location inside the medieval Antonierhaus on Martin Luther Square.

Hotel Weisses Ross (doubles from €103) has rooms in its 600-year-old original building, plus modern ones with great rooftop views. There is the obligatory Christmas market and snowy slopes for skiing and snowboarding are within easy reach at Oberstdorf. Plus, of course, only an hour’s drive is Neuschwanstein, the ultimate crazy king’s castle, built by Ludwig II before he was arrested for, among other things, poor table manners.
• Ryanair flies from Stansted from £42 return

Sibiu, Romania

Sibiu really was designed for romantic winter getaways: good snowfalls, winding cobbled streets, medieval towers and a custom of going overboard on festive lighting. This is a great town to amble around, discovering ever more quaint medieval buildings that serve food and drink.

At the stunning wooden Crama Ileana restaurant mămăliga, polenta with cheese, is the traditional starter, and ţuică, plum brandy, the inevitable finish. For the local speciality, tripe soup (ciorbă de burtă), a dish that is hard to do well, unpretentious Kon Tiki (on Facebook) is the aficionados’ favourite. The squeamish might prefer coffee and cake at Arhiva de Cafea și Ceai on Strada Arhivelor.

The town’s focal point is the historic Piata Mare (Big Square), with historic walls and towers to explore. The Bridge of Lies, built in 1859, is still standing despite the superstition that if a fib is uttered while crossing, it will collapse. The Lutheran Cathedral of St Mary’s has colourful decor and astonishing tombstones, including that of a local lad, Prince Mihnea the Bad, son of Vlad the Impaler.

A good budget stay is Smart Hostel (dorm beds from £9, doubles from £24); more upmarket is Levoslav House (doubles from £55), a boutique hotel in a centrally located 19th-century villa. For winter sports, Păltiniş is 10 miles away; in summer it becomes a trekking area. Motorists and cyclists won’t want to miss the Transfăgărășan Highway, the monumental tarmac folly former leader Nikolai Ceauşescu built across the Carpathians.
• Wizzair flies to Sibiu from Luton from £42 return