Tihany Peninsula

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

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.

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.

The hilltop fortress that withstood the 1552 Ottoman siege, with casemate tunnels, a museum and ramparts over the town.

A neo-Gothic riverfront parliament of 1902, the largest building in Hungary, visited on timed guided tours through the dome hall and staircase. Completed in 1904 on the Danube bank, it is one of the largest parliament buildings in Europe. Guided tours show the grand staircase and the Holy Crown of Hungary.

A terraced neo-Romanesque lookout on Buda's castle hill, with seven turrets and a panorama across the Danube to Pest. The neo-Romanesque terraces were built between 1895 and 1902 on Castle Hill next to Matthias Church. Their seven towers represent the Magyar tribes, and the walls give some of the best views of the Parliament across the river.