There is fantastic hiking in Arizona of all abilities. If you stay near Tucson check out the Sonoita area for wineries.
As stated above, pick a few areas and try them out. Every state park is great. In Tucson, give Gilbert Ray campground in Tucson Mtn. Park a try. It's beautiful Sonoran desert with easy hikes. It's close to the Desert Museum and Saguaro Nat'l Park - West. (There's also a East area, too.) Tucson's Catalina State Park is very nice.
For the greater Phoenix area try the scenic Maricopa County parks for big sites, lush vegetation and nice hikes. Lost Dutchman State Park in nearby Apache Junction is also a good one.