Our favorite thing we did in Sarajevo was visit the abandoned bobsled track on Mt. Trebevic. The track was built for the 1984 Olympics and was damaged during the Bosnian war, when it was used as an artillery position for the Bosnian Serb forces. Now it is covered in graffiti and is a pretty surreal, post-apocalyptic sight in the forest.
After lunch at the adorable Dveri restaurant, we started up the very steep hill toward the mountain. This was a really strenuous hike where, whenever the road forked, the answer was always to take the steeper path.