Wander across the Chain Bridge up to the Castle District and enjoy the fabulous vistas of Pest and the Danube. Get away from the crowd and have a rest on a bench on Tóth Árpád promenade while the hills of Buda surround you. Make sure to visit the courtyards of the Royal Palace, Matthias Church and the Fisherman's Bastion.
When it's time for lunch, have a Goulash soup in one of the numerous Hungarian restaurants such as Hadik, 21, Pest-Buda or Arany Hordó. Once back in Pest, stroll down Andrássy Avenue towards Heroes' Square, or alternatively, use the historic Millennium underground. On your way you'll see palaces, the former Parisian department store, the Opera House and the House of Terror, a museum located in the former headquarters of the communist secret police.
Two major art museums are on the large Heroes' Square, at the end of the avenue. The lake in the City Park becomes an ice-skating rink in winter, while in summer you can rent a boat or try wakeboarding there. Vajdahunyad Castle, the zoo and the Széchenyi spa are nearby.
The thermal baths are perfect after an exhausting day of sightseeing. If you feel more like buying something, discover the shopping streets of the 5th district. In the evening, enjoy dinner at Liszt Ferenc square or a concert at the Music Academy which is tucked away at the other end of the square.