Gornji Grad is the upper and medieval part of the city. A huge fire destroyed a lot of the old upper and lower town but surviving it was a painting of the Virgin Mary which is now part of a shrine made of the Old Town Gate. It’s now a place of pilgrimage for many and you should be respectful passing through it.
The Montmartre of Zagreb is called Strossmayer’s Walkway and is full of artists painting and displaying their work, street entertainers, curio sellers and more. It’s got a magical atmosphere, especially at night or in the cold of a winters evening.
Whilst Zagreb is inland it doesn’t mean that you can’t enjoy a swim or lie on a beach. There are two lakes close to the city; Jarun and Bundek. Jarun is the party beach whilst Bundek is a more refined area which also hosts exhibitions in the beautiful gardens that surround the lake.