Any direction you go will be fun. If you wanted to stay local the Mcdowell park has no shortage of fine ST and places to camp. If you desire more back country... the sky is the limit. Check out the Black canyon trail, Look into the Arizona Spring Fling, Some of the Arizona endurance series events, the Arizona trail, Crown king, Sedona, plenty of stuff on the west side of town, south mountain, Tucson. Just get here and throw a stick, you just can't go wrong.
Good Luck!- JF