Budapest, Hungary’s capital, is bisected by the River Danube, and the 19th-century Chain Bridge connects its hilly Buda district with flat Pest. A funicular runs up Castle Hill to Buda’s Old Town, where the Budapest History Museum traces life from Roman times onwards. Trinity Square is home to 13th-century Matthias Church and the turrets of the Fishermen’s Bastion, which offer sweeping views.