It depends on how "not improved" you're talking about and which day of the week.
If during the week, I would bet you could camp almost anywhere in any urban canyon without having close neighbors, or anywhere in the Uintas with ease. On a friday/saturday, all bets are off.
One out of the way place I liked, although somewhat far away is Granite Creek in the Deep Creek Range out on the NV/UT border south of Wendover. Long gravel roads are necessary to get there, and there are no facilities available all the way out there. Just some farming communities or less. There are no campgrounds really, but you'll get away from crowds for certain.
An interesting place to see if you haven't yet is City of Rocks in Idaho. It isn't far into Idaho either. It is a lot of fun and really cool to see.