Tihany Peninsula

Balaton is central Europe's largest lake, shallow enough to warm quickly in summer, with a busy southern shore of resorts and a quieter northern shore of volcanic hills and vineyards. Ferries cross between the two, and a cycle path circles the whole lake. Tihany peninsula and the basalt hills behind Badacsony hold the best views and wine.

A neo-Gothic riverfront parliament of 1902, the largest building in Hungary, visited on timed guided tours through the dome hall and staircase.

A terraced neo-Romanesque lookout on Buda's castle hill, with seven turrets and a panorama across the Danube to Pest.

One of Europe's largest medicinal bath complexes, with outdoor pools fed by thermal springs and indoor sauna and steam rooms.

District VII, holding Europe's largest synagogue, a memorial garden and the ruin bars built into unrestored courtyard buildings.

Eger is a Baroque town in the hills of northern Hungary, known for the castle that held out against an Ottoman siege in 1552 and for the Egri Bikavér red blend. Cellars cut into the rock of the Szépasszony valley on the edge of town pour directly from the barrel. The centre is small, walkable and noticeably cheap.