+1 for S mountain, that would be your narliest trails near town
trail 100 is an easy desert roll right in town. Ride to the mountain park and then climb Squaw Peak.
Mcdowell Mtn park has tons of trails (near fountain hills) including the old cactus cup race course. But I would skip the race course and head into the hills.
I haven't been there yet but rumor has it the Black Canyon section of the Arizona trail (NW of the city) is fantastic. It looks like you can ride a 15 mile lollipop from a trail head just off us17.
Cave Creek area has trails, dynamite trail is ok. But it does have the brewery, so there's that.

You really can't go wrong riding anywhere in the desert, be sure to take water, 2 tubes and, we find tequila works better than whiskey in the big sandbox that is Phoenix. Lot's of Beach No Ocean
have fun