Neither Buda nor Pest though part of district XIII, 2.5km-long Margaret Island in the middle of the Danube was always the domain of one religious order or another until the Turks arrived and turned what was then called the Island of Rabbits into - appropriately enough - a harem, from which all 'infidels' were barred. It's been a public park since the mid-19th century.
Like the Buda Hills, Margaret Island is not overly endowed with important sights and landmarks. But boasting a couple of large complexes, a thermal spa, gardens and shaded walkways, the island is a lovely place to head on a hot afternoon.
Margaret Island is a great spot for sports and other activities, and you could spend the entire day here cycling, swimming or just pampering yourself at the Danubius Grand Hotel Margitsziget, one of the most modern spas in Budapest.