Hop aboard tram no.2 along the embankment of Pest for great views of the Buda Hills and the enormous neo-Gothic Parliament building, the world's second-largest, scenically reflected in the Danube. Then stroll along elegant, tree-lined Andrássy ut, a boulevard conceived to rival Paris's Champs-Elysées. It’s lined by swanky cafés and grand architecture, including the State Opera House.
Follow Andrássy út to Városliget Park (City Park), home to Budapest’s quirky zoo and botanical gardens with its oddball National Romantic buildings. The Városliget is also home to several outdoor cafés and the fairy-tale Vajdahunyad Castle, featuring scale models of buildings from around Hungary, especially Transylvania (now in Romania). In winter this castle is the spectacular backdrop to an ice rink; in summer its lake offers pedalo and rowing-boat hire.
Cross the river and head for the heights – the Buda Hills are a breath of fresh air away from the bustle of Pest, with nature trails, bike hire, caves, and restaurants with leafy terraces. Get there by funicular railway, then seek out the Children’s Railway running 11km through the forest. Not only for kids but run by kids, ‘the greatest toy in the world’ was founded by the Communists in 1949, for their Young Pioneers. These days it’s local schoolkids aged 10–14 who control the station and the daily traffic, printing tickets, operating signals and switches, and looking after passengers while employees of the Hungarian State Railways drive the diesel and steam engines (the kids get one day off school every two weeks). The 35-40min ride allows you to see foxes, deer and wild boar within a national park; if you wish you can get off at various stations and walk forest footpaths, climb lookout towers, ride a chairlift, explore a ruined medieval monastery, and visit a game reserve. There’s also a museum about the ‘railway children’.
Continue the theme by heading to the outdoor Hungarian Railway Museum back in Pest, where you can admire vintage engines, drive an engine, and ride on a narrow-gauge children’s railway, a turntable, a horse-tram, a rail-cycle, and a Tchaika car that was customised to run on railway lines for use by mechanics.
Bathe. Budapest has 40 Turkish-style baths and outdoor pools, including the Gellért Baths behind the Gellért Hotel, famous for their Art Nouveau interiors. As well as men’s and women's pools, saunas and steam rooms, there are outside pools, including one with a wave machine. Or try the Széchenyi Baths in the Városliget (see above), with outdoor pools in a vast neo-Baroque courtyard with classical statuary. It’s a surreal experience seeing people play chess as they soak, or bathing outdoors at night or in winter, surrounded by snow. Other child-friendly lidos or pools include the summer-only Palatinus Furdo on Margaret Island and Dagaly Furdo by Arpad Bridge.
Near Széchenyi Baths, Hősök tere or Heroes' Square has iconic statues representing national leaders including the the Seven Chieftains of the Magyars.
Take to the Danube, the legendary river slicing through the city, by canoe, rowing boat or cruiser, or even by wakeboard or waterskis. Or go mad on Margitsziget (Margaret Island), a car-free urban playground in the middle of the Danube, with a sports stadium, tennis courts, the huge Palatinus outdoor waterpark, an open-air theatre, Japanese and rose gardens, and early-medieval ruins. Oh, and two spa hotels and a beer garden. You can get around the island by Bringo cart, a quirky 4-person bicycle with kids’ seats on the front, or there are standard bikes to hire as well as electric cars and Rollerblades.
Take in some culture. There’s a triple whammy of art, history and architecture at the Buda Royal Palace on Castle Hill, dating back to the 14th century and housing the Budapest History Museum and the Hungarian National Gallery. From there it’s a short stroll to the Fishermen’s Bastion (Halászbástya) near the Royal Palace, with medieval-looking minarets and walls and incredible city views. Back down in Pest, the Museum of Ethnography celebrates Hungarian folklore through exhibitions of artwork, photography, clothing and jewellery.
If that’s too highbrow for your children, check out the Palace of Wonders (Csodák Palotája) in the lovely Millenáris park in Pest, a hands-on science and technology museum. Also in Pest, at 60 Andrássy út, and strictly for older children, the House of Terror is an old Nazi and then Communist secret police HQ converted into a museum. You can explore the cellars in which prisoners were tortured and see some of the instruments used. If the experiences makes them curious about life under ‘Big Brother’, take them to Statue Park (Szoborpark) outside the city confines (buses go direct from Deák tér), a cemetery containing monolithic statues of Marx, Engels, Lenin and other Socialist figureheads.
Go shopping. As well as American-style malls, Budapest has a good fleamarket and many market halls where you can stock up on delicacies, from smoked sausages and salami to pálinka (fruit brandy).
Branch out – both the Austrian capital Vienna and the Slovakian capital Bratislava can be visited by hydrofoil from Budapest. Or you can bike along the Danube from Vienna to Budapest.
Less ambitiously, Vadaspark Wildlife Park 18km west of Budapest has wild animals from wider Hungary and Europe as a whole, including wolves, foxes, deer and hedgehogs, plus a play area. Thirty kilometres northeast of the capital, meanwhile, and easily reached by the commuter railway (HÉV), is little Gödöllö, home to a Baroque royal palace that once belonged to the Habsburgs. It’s an atmospheric place to bring a picnic, especially when there’s a concert on.