Well, depends on how adventurous you are (and how much time you have). If you head way North and West, and actually start in Mesquite, NV, you can go South and East into the Parashant Wilderness. Savanic Mine, Grand Gulch Mine, Twin Point, Bar 10 Ranch, etc.
Some of the most impressive scenery I've been to (especially Twin Point). However, this is a 3 day trip (at least). The trails range from real easy to nasty.
I surmise, however, that you're looking for something close to home. The "Arizona Off-Road Adventures" book has lots of information. I'm sure there are others.
Gotta get down to the Cumberland Mine
That's where I mainly spend my time
Make good money, five dollars a day
Made any more, I might move away