Grand Canyon is surrounded by Kaibab National Forest and offers great UTV adventures. 

The Kaibab National Forest Motor Vehicle Use Map (MVUM) shows where it is legal to drive a motor vehicle on Kaibab National Forest. Having an MVUM is as necessary for motorized travel as having game proclamations when going hunting. 

Although other travel aids or more detailed maps may be used in conjunction with the MVUM, it is the MVUM itself which is the reference document for where it is legal to drive a motor vehicle. Click here for the most up to date MVUM's.  Always check for latest MVUM's at their site - they also offer a great GPS enabled map that is highly recommended but it is adviced to download prior to your arrival.

For a visual now on how many roads are available here is a good overview map that is a smaller and easier to take with.