The City Park (Varosliget) is on the Pest side, and is a wonderful place for families and lovers alike to spend an afternoon or evening. You can row a boat out onto the large lake, take a thermal bath, visit the zoo, or the museums.
It's home to Heroes Square (Hosok tere), with its monument to the 1956 Uprising and the Millenary Monument that depicts the Angel Gabriel offering Stephen the crown to the Kingdom of Hungary, surrounded by statues of the seven leaders of the original Magyar tribes.
The City Park also contains the Museum of Fine Arts, the Palace of Art, the City Zoo, the Szechyeni Bath, and the Municipal Great Circus. Also in the park is the Vajdahunyad Castle, located on an island in the lake. The park is full of playgrounds, sports fields, small gardens, and a manmade lake.
A word of warning for the prudish--even the not-so-fit lillt old men lie around the park sunbathing in very little clothing.
Outside the nearby Jak Chapel is a statue of a hooded monk called Anonymous, who chronicled the activities of the early Magyar tribe.