Tucson is a good base for the saguaro desert in every direction. Saguaro National Park sits on both sides of the city, and within an hour or two you can reach copper-mining ghost towns, Spanish missions in the Santa Cruz valley, and the cool pine forests of Mount Lemmon.
The classic loop south — Tubac and Tumacácori on the way to Nogales and the Mexico border — makes a good day. East, Colossal Cave and Saguaro National Park East fill an easy afternoon. North, Catalina State Park and the mining town of Oracle. Southeast, the historic mining and gunslinger town of Tombstone, about 75 miles.
For something more adventurous, drive up Mount Lemmon — an hour from town climbs through five vegetation zones to pine forest at 9,000 feet, with hiking trails, a small ski area in winter, and excellent stargazing at the Mount Lemmon SkyCenter.