Ventana and Pima Canyons are also nice, and right next to town on the northside. At Sabino Canyon, I'd also recommend taking the Bear Canyon shuttle bus to the Bear Canyon/Seven Falls trail. I guess I like Seven Falls just about the most of any hike that is right next to town. As I recall (I moved away from Tucson almost 9 years ago, yikes!) the Seven Falls trail is about 2.5 miles one way, IF you ride on the shuttle bus. Add about another mile each way if you walk from Sabino parking lot. Seven Falls is so spectacular it would be a national park or something if it were somewhere else. It is also very popular, a good thing for you when you are new to the area, because there will be people to direct or help you if needed.
There is a point of no return unremarked at the time in most lives. Graham Greene The Comedians
Steal your face right off your head!