Croatia's sixth-largest cave is open for visitors on weekends from mid-April through the summer months. You can explore the first 380m of the cave on an hour-long guided tour that takes in some weirdly shaped stalagmite formations and fossils. It's located in the western part of Medvednica, which is also home to Glavica Mountain Hut.
To reach the cave from Zagreb, take city bus 124 from Črnomerec to Gornji Stenjevec (about 15 minutes). Then walk by the Dubravica stream uphill to Veternica for about 20 minutes on the trail marked 3 (it's another 15 minutes to Glavica).