South Mountain Park is awesome! Great hiking and mountain bike trails. I've hiked just about every marked trail and many that aren't.
Hidden Valley (Fat Man's Pass) is probably the most interesting as a nice diversion off the National Trail. In the winter, I hike quite a bit in the western part of the park and rarely see people which can be nice if you are looking for quiet.
Telegraph Pass is a favorite from the south while the Central Avenue or 24th street locations are most popular from the North. The busiest parking lot and a great place to people watch as well is the entrance from 48th street to the east.