Why you should go: Budapest is less expensive and less explored than other Western European capitals. It has the beautiful Buda Castle, and the Danube River divides the city, Buda from Pest.
Where to sleep: The Opera House and museums are in Central Pest, but staying in Buda can be cheaper. The Hotel Astra (ohb.hu/astra/index.en.html) is in central Buda, not far from downtown Pest. Vadvirág Panzió (hotelvadviragpanzio.hu) is a steal in nearby Buda Hills, but you'll have to take a bus into town.
Where to eat: Have coffee and a pastry at the popular Ruszwurm. For dinner, try the traditional Tabani Terasz. "It's below scenic Castle Hill and is still largely undiscovered by tourists," says Ben Curtis, a leader for Rick Steves's tour company, Europe Through the Back Door.