An eye-shaped haven in the centre of the Danube, Margaret Island lies between the grandeur of Pest to the east and Buda, the city’s more frenetic side, to the west. Just 1.6 miles long (it is linked to a bridge at either end) and less than half a mile wide, it’s a tree-lined sanctuary away from the crowds. And, best of all, it’s (mainly) free.

Church ruins on the island. Photograph: Alamy

Most of the island is landscaped parkland and there’s a rose garden in the middle, plus a small Japanese garden near its northern tip, with a fishpond and waterfall. A grand musical fountain near the Margaret Bridge at the south end comes alive four times a day, its jets dancing to classical and contemporary tunes. We hear George Ezra’s 2014 song Budapest through the trees on the afternoon we visit; it’s somehow more charming than corny.

The island’s water park. Photograph: Alamy

History buffs will like the ruins of a medieval church and nunnery, while the art nouveau water tower is sure to fill up many visitors’ Instagram feed. Most of the island’s delights are free but there are charges to go up the tower and to swim in the outdoor water park, which uses water from thermal springs. There are also electric golf carts for hire.

Despite the attractions, there’s space for peace and quiet: seek out a shady patch by the riverside for a picnic and get a different perspective on the big city.