Go to the Mesa ranger station
Mesa Ranger District
5140 E. Ingram St.
Mesa, Arizona 85205
(480) 610-3300

It's near Falcon Field in east Mesa, There you can get free passes for the trails in east Mesa/Apache Jct as well as maps. Try out Bulldog canyon for a quick, easy, scenic 4 wheeling. You can do it from the salt river to north apache jct or shorter easier runs between the river and Usery pass.
Then there's the Rolls recreation area near Saguaro lake, free access no passes but get a map at the ranger station because route finding has gotten complex out there with all the ATV/SXS/dirtbikers making tons of new trails everywhere. The Rolls is pretty easy but can get off camber and tippy easily because the hills are rutted out so badly.
The road over 4 peaks to Roosevelt lake is easy when there's no snow and it's not too far north of town.