Few cities in the U.S. can claim to be 'sandwiched' by a National Park; Tucson might well be the only one. Saguaro National Park is divided into Eastern and Western divisions that flank the city--plenty of wilderness hiking within a half-an-hour's drive from the middle of town.
If you're here, like most visitors, in the winter, a perfect half-day's hike is up to Wasson Peak in Saguaro National Park, on the western edge of the city. Seven-miles round-trip with a nearly 2000-ft elevation gain: it's a moderate climb with 360-degree views from the top. (You do NOT want to hike this in the summer; there is no shade.) At 4687ft/1428m, it's low compared to some of the 9000+ ft peaks on Tucson's other horizons, but the panoramas are unbeatable, and the trek up through a saguaro forest is unforgettable.
There are several routes, but perhaps the most popular is the Kings Canyon trailhead--directly across the road from the Arizona-Sonora Desert Museum. Hike the peak in the morning (give yourself around four hours so you can enjoy lunch and the view from the summit), and spend the afternoon visiting the animals across the road. (A new aquarium featuring the Sea of Cortez just opened; fall through spring also offer 'raptor free flight' demonstrations.)
(From the top, the views: trail to the peak, looking south toward the distant Santa Rita mountains, looking over the NW part of the city to the forested peak of Mt. Lemmon in the Santa Catalina Mtns.)