The for the most part car-free Margit sziget (Margaret Island) sits in the Danube between the Margit and Árpád bridges and is Budapest's loveliest park. It was a center of religious contemplation from the 11th century onwards and includes the ruins of two monastic churches and the convent of Princess Margit, daughter of King Béla IV, along with a 1911 water tower, thermal baths, athletic facilities and biking paths. We covered the entire length of the island (2 miles) on foot along the main road and took a bus back to Margit Bridge, but it's definitely a place to go back to as I know we missed some of the sights (plus it's just a very pleasant place to spend an afternoon). I do think, though, that it might be a good idea to rent some of the various forms of transportation available because it's really difficult to cover everything on both sides of this long and wide island on foot.