I like the McDowell Mountain Race Loops in Fountain hills. There are three loops to ride - the Sport Loop, which is very short (3 miles) but really fast and very fun. Technical Loop, and the Long Loop. Five dollar entrance fee, but the park is well maintained, single direction and well worth it. It was designed partly by Specialized and the Mt bike races are held there.
I also like South Mountain. The desert classic is a fun 14 mile out and back, but there are other trails like telegraph and the mormon loop that are more technical. The park is 22 square miles. Access off 48th street is closed for park renovations, but there are many ways in. Lots of local night rides there can be found on meetup sites, possibly thru local bike shops.
Hawes is a trailhead located off Power Road (Bush highway) just past the canal on the east side of the road. There's good parking on the west side of the street, but better parking at Walgreens down the road. Thats near the salt river and Saguaro lake. Lots of activity out there on Saturday morning. There are extensive trail systems on Pima and Dynamite in North Scottsdale too. You won't get away from loose rock and ledges in regards to technical in the desert (locally). Up north a little ways in Sedona, the trail systems are a totally different kind of terrain. There, you are above 6000 feet sea level. There is water eroded rock, dirt and trees unlike the desert down here. There is very technical stuff in Sedona. Its only 1.5 hours to get there. Its a day trip or a weekend trip.
Check out the bike and bean coffee shop in Sedona. They have lots of information about local trails (a 3-d model of the are and trails and the employees are all bikers). There really isn't a much better place to ride in AZ as far as sights. If you are ever back during the summer (or better yet the fall), Flagstaff is an awesome place to ride. Air is thin up there. If you have a friend and a second vehicle, you can start at the top of Mount Elden at 9000 feet. It is fun as shit to travel 7 miles down hill and drop 3000 feet in no time. Switching back and forth thru a thick forest on the mountain with huge drops and roots. Only to come out into a large field and rip along an old fence line. In the spring, as the snow melts, the area has a strong smell of pine. Right now you can ski up there and come back to shorts weather the next day LOL.
A good resource is Mountain bike AZ.com. Thats a good place for directions and reviews of trails and skill levels.