South Mountain is a great place for a nice hike within the Phoenix metro limits. Remember your location if you are disappointed by the fact that many hikes intersect with roads and that Phoenix is almost always in view. This is one thing Phoenix has done right. A 10-15 minute drive from my apartment and I can observe several types of cacti, and maybe even some desert creatures. There's usually a nice breeze blowing from the peaks, and looking out away from the city gives one gorgeous views of the southern metro farmlands and beyond.
Although I like to take my time hiking, South Mountain gives you the opportunity for a full hike including transit there and back in about two-and-a-half hours. It's a really good introduction to the desert for anyone visiting town, and there are various types of trail suitable to both those in shape and those not so much.