The wooded slopes of Mount Medvednica, or “Bear Mountain”, offer the easiest escape from the city, with the range’s highest peak, Sljeme (1033m), easily accessible on foot or by road. The summit is densely forested and the views from the top are not as impressive as you might expect, but the walking is good and there’s a limited amount of skiing in winter, when you can rent gear from shacks near the top.
However you arrive on Sljeme, its main point of reference is the TV transmission tower, built on the summit in 1980. The tower’s top floor originally housed a restaurant and viewing terrace, but the lifts broke down after three months and it’s been closed to the public ever since. A north-facing terrace near the foot of the tower provides good views of the low hills of the Zagorje, a rippling green landscape broken by red-roofed villages. Just west of here is the Tomislavov Dom hotel, home to a couple of cafés and a restaurant, below which you can pick up a trail to the medieval fortress of Medvedgrad (2hr). Alternatively you can follow signs southwest from Tomislavov Dom to the Grafičar mountain hut, some twenty minutes away, where there’s a café serving basic snacks.