Hey there San Tan friend. There's so much hiking and camping in this state it's hard even make a list. The Oak Flats campground just east of Superior is an hour or less from Tempe and probably even shorter for you to get to. It's a free public campground and the are around it is pretty amazing. The rock is incredibly featured and one of the best areas in the state for rock climbing. I've wanted to . Pic is from there.
As for shooting, I also used to go shoot in the desert east of the 79 and south of the 60. Around here:
https://maps.google.com/?ll=33.229785,-111.287642&spn=0.062103,0.132093&t=h&z=14 