We live in Tucson and DH hikes nearby at least twice a week. All of these are within an hour's drive of Tucson.
I'll let you Google details. As far as camping comfort, timing is everything, since elevation will determine temps.
We've been here two years and have barely scratched the surface! So many varied landscapes so close together. And the Sonoran desert is a revelation.
Hikes with elevation gain:
Catalina State Park: Romero Pools Trail
Madera Canyon (some free camping nearby)
Most trails on Mt. Lemmon (the higher up the mountain, the more trees there are!)
Wasson Peak
Agua Caliente trail
Sonoran desert and grassland hikes:
Sweetwater trailhead
Las Cienegas National Recreation Area (just about anywhere, free campgrounds and dispersed BLM camping )
Tucson Mountain Park
And further east you must check out the Chiricahuas. Probably too cold now, but come Spring they will be lovely.