Base yourself in Žabljak, Montenegro's highest town, and the whole park is on your doorstep. The gentle introduction is the Black Lake (Crno jezero) — a 3.5 km forest loop around still, dark water beneath the peaks, easy enough for anyone and stunning in the morning calm.
With more time and stronger legs, push higher: the trail toward the Škrčka lakes or up toward Bobotov Kuk, the highest summit, opens into alpine meadows and those glacial 'mountain eyes' the range is famous for. Weather turns fast up here — carry layers even in summer.
Round the day off on the drive back via the Đurđevića Tara bridge, or with a bowl of hearty mountain food in town. In winter the same slopes become Montenegro's main ski area.