October through May is the best time to explore the area's 35 trails. The Peralta Trail is arguably the best marked, most traveled path with the most easy scenic rewards, so if you're new to the 'hood, this might be your best bet.
After tackling Peralta, you can move on to the more isolated trails. Just be extremely careful. Tell someone where you are going and bring plenty of supplies, especially water. Hikers can be lulled into thinking of the Superstitions as an easy day hike just outside town. But this is a different world. You need to be prepared.
Okay, lecture over. Enjoy!