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

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

Bratislava, the capital of Slovakia, is set along the Danube River by the border with Austria and Hungary. It’s surrounded by vineyards and the Little Carpathian mountains, crisscrossed with forested hiking and cycling trails. The pedestrian-only, 18th-century old town is known for its lively bars and cafes. Perched atop a hill, the reconstructed Bratislava Castle overlooks old town and the Danube.

Vienna, Austria’s capital, lies in the country’s east on the Danube River. Its artistic and intellectual legacy was shaped by residents including Mozart, Beethoven and Sigmund Freud. The city is also known for its Imperial palaces, including Schönbrunn, the Habsburgs’ summer residence. In the MuseumsQuartier district, historic and contemporary buildings display works by Egon Schiele, Gustav Klimt and other artists.

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