About 20 miles west of you off State Highway 238 is the Maricopa Mountains Wilderness in the Sonoran Desert National Monument. This is a neat area to explore, spring is the best time in my opinion. Also, from the town of Mobile, about 10 miles west of you, you can take a series of dirt roads north (get a map) to the Sierra Estrella Wilderness. Fantastic hiking here; very rugged though. A little further north is the Estrella Mountain Regional Park which I believe has some competitive tracks for mountain biking. South Mountain Park just a short jaunt up I-10 is great for mountain biking, very rocky though. Hope this helps.
"I'm not a vegetarian because I love animals; I'm a vegetarian because I hate plants." A. Whitney Brown