You are bound to find a number of great places in Arizona where you can ride your 4-wheeler. The valleys and flat lands are great for really opening up your 4-wheeler. The Sonoran Desert area formed where the Yellow Medicine meet the Gila Bend Mountains, forms a great valley to explore with your 4-wheeler.
The Crown King Area is about 35 miles north of Phoenix, and you will find everything from old mines to some great winding trails in the area. Be cautious of old mines and only explore from the outside, they can have bats or toxic gases inside. The Ehrenberg Sandbowl is another popular place to ride your 4-wheeler with beautiful hills, sand and a web of trails to ride around.
If you have newer 4-wheelers in your group, the east trails are located at Route 66. You will find 42 miles of this road from Kingman to Topock, at the California border. Lake Havasu has many areas for exploring trails on your 4-wheeler, while Sedona and Flagstaff are also popular spots for riders.
If you're a beginner, the "tot lot" at Hayfield Draw is a great place to start and once you get your confidence up, the Hot Wells Dunes Recreation Area has 2000 acres of rolling sand dunes for lots of open riding. Tonto National Forest has two areas that are specifically dedicated for 4-wheeler use, Rolls OHV Area and Bulldog Canyon. Vermilion Cliffs Highway has 277 miles of 4-wheeler trails that wind through small rural communities and a Navajo Indian Reservation on the east.