The most important sights of the city can be found here, on the right bank of the Danube. Buda is the capital city's green belt with popular hiking destinations like the János-hegy ('hegy' meaning 'hill'), Normafa, Széchenyi-hegy, Kis- and Nagy-Hárs-hegy, Remete-hegy, Hármashatár-hegy and the Game Park in Budakeszi, all of them parts of the Buda Nature Reserve.

The Castle District in Buda

Erected in the 14th century and rebuilt in the Baroque style 400 years later, the Royal Palace at Szent György tér was the residence of the Hungarian monarchs for 700 years. Today it houses Budapest's most frequented museums and galleries. The Hungarian National Gallery (Buildings B, C, and D) offers a selection of the history of arts in Hungary from the 10th century to the present day. Exhibits include a collection of early medieval and Renaissance stone works, Gothic wood-carvings, panels and triptychs, Renaissance and Baroque art, 19th- and 20th-century painting, sculpture and collections of coins and medals. Guided tours are available to the crypt of the Hapsburg viceroys. At the History of Budapest Museum (Building E) restored sections of the medieval royal palace in Buda, its chapel and Gothic sculptures as well as permanent and temporary exhibitions on Budapest's history can be seen. The National Széchényi Library (Building F), the country's largest library, houses - among others - a rich collection of the Corvinas, medieval codices from King Matthias' library. In Building A the Museum of Contemporary Arts, also known as the Ludwig Museum, displays the works of outstanding Hungarian and foreign contemporary artists.

Topped by a tower of stone tracery, Matthias Church, also called the Church of the Blessed Virgin Mary, was the scene of coronations and royal weddings. In the early 19th century it was rebuilt in a neo-Gothic style. Its crypt now displays a collection of ecclesiastical artefacts. From spring to autumn concerts are organised here. The Fishermen's Bastion, a neo- Romanesque bulwark with seven towers built on medieval walls, offers an excellent view of the city. Further back the remains of the 13th-15th-century St. Nicholas Church with a Dominican monastery. The urban middle-class houses in the streets connecting Bécsi kapu tér and Dísz tér, gates to the Castle District, were built on medieval foundations. The Gothic sedilia of their doorways lend a unique feature to them. The Castle Cave, a 1,800-m section of the 12-km cave system under Castle Hill is open to the public only by booking in advance. The Military History Museum displays memories of Hungary's military past, and the medieval Jewish Chapel  offers an insight into the past life of the Jews in Buda. The Baroque Erdődy- Hatvany Mansion keeps rare musical instruments from the Museum of Musical History as well as a rich collection of the manuscripts of the great Hungarian composer Béla Bartók (1881-1945).

Gellért Hill

Not many cities have a hill rising from the city centre and protected as a national park. Gellért Hill has a fortress called the Citadel on top of it, which was built in 1851, and is now a tourist attraction with terraces offering the fullest panoramic view of the city.
Other monuments from the Turkish period include the tomb of Gül Baba, a Muslim shrine on Rózsadomb ('Hill of Roses'), and the domed Király BathsThermal, with facilities including thermal pools, tubs and steam baths.
Fertile hillside vineyards have made Budafok in the south of Budapest a city of wine and sparkling wine. Its highlights include a labyrinth of cellars and the Museum of the Törley Sparkling Wine Manufacturers. The Szoborpark (Park of Sculptures) at the junction of Balatoni út-Szabadkai út displays an unparalleled collection of socialist-era public sculptures. The Castle Museum in Nagytétény has an interesting collection of furniture.