Here are some of my favorite spots I've visited so far.

The Strip, West Central Utah

This lake is an intermittent and endorheic area which lies in the near lowest part of the Sevier Desert, Millard County, Utah. Like the Great Salt Lake and Utah Lake, it is a remnant of Pleistocene Lake Bonneville.  The area is owned by the BLM and  has easy, free access. This is also the Ibex Hard Pan Backcountry Airstrip.  Since pilots generally land to the south of the island, camp on the area north of the island.  There is marginal cell service (AT&T).

GPS coordinates to the lake's entrance: 38.986629, -113.365624
Travel time: 9 hours from Boulder, Colorado

The Edge, East Central Utah

This plateau is a really an amazing spot to camp.  It's very secluded: there is no one or anything for miles.  You'll need a car with a little clearance to make it to the top; it's worth it.  Just be careful not to walk off the edge -- it's a really long way down. There is marginal cell service (AT&T). 

GPS coordinates to cutoff to plateau: 39.209022, -109.292559
Travel time: 6 hours from Boulder, Colorado

38.83617239935396, -113.22963400117375
38.94134569900622, -113.23183319673515