Every visitor to Budapest walks along the River Danube, and for good reason: liquid history flows below and spectacular views greet you at every turn. On the west bank is Buda, on the east Pest. Pest’s street layout features Habsburg-style ring roads, joined by important spokes, such as Andrássy út, the tree-lined boulevard that begins next to the monument to the nation’s leaders at Heroes’ Square (Hösök tere). Further up is the House of Terror Museum (VI. Andrássy út 60, 374 2600, www.terrorhaza.hu, closed Mon), a sobering exhibition about oppression in a building once used by Nazis and, later, the communist secret police. Continue downtown to find the opulent Opera House (VI. Andrássy út 22, 353 0170), built in 1884 by Miklós Ybl, and the basilica (V. Szent István tér, 317 2859), named after St Stephen, whose mummified right hand is inside.

On the river, three blocks from the basilica, is the Chain Bridge (1873), the first permanent crossing between Buda and Pest. The Buda side of the bridge is at the foot of the main tourist sights of Castle Hill. On the hill, the Royal Palace complex houses the vast Hungarian National Gallery (224 3700), the National Széchényi Library (224 3848), Matthias Church (I. Szentháromság tér 2, 355 5657) and the Fishermen’s Bastion, which offers superb views of the city.

A few blocks north of the Chain Bridge, on the Pest side, is the Parliament building (V. Kossuth Lajos tér, 441 4904). This structure, along with much of central Pest, was built in the late 19th century, during Hungary’s heyday as a partner in the dual monarchy with Austria.

Other periods have clearly influenced the look of the city, including the period of Habsburg domination, when the castle district was built, and the 16th-century Ottoman occupation, which produced Turkish baths like Széchenyi (XIV. �llatkerti út 11, 363 3210) and the newly renovated Rudas (I. Döbrentei tér 9, 356 1322). No prizes for guessing who was responsible for the hideous apartment blocks that stud the outskirts of the city.

Further sites of note include the world’s second largest synagogue (VII. Dohány utca 2, 413 5500) and the new Holocaust Memorial Centre (IX. Páva utca 39, 455 3333, www.hdke.hu).

• Tourist information: V. Sütö utca 2 (438 8080, www.tourinform.hu).