We found 2 Reddit comments about Utah Byways: 65 of Utah's Best Backcountry Drives. Here are the top ones, ranked by their Reddit score.
Most of the wasatch front area is watershed so your going to run into problems finding places.
As already mentioned there is five mile pass. Been there a couple of times. It is better for 4wheelers but it is fun in a jeep/suv.
Theres the pony express trail out that way as well.
Dunes and such- try knoll's.
A more serious rock crawling place exists west of utah lake called mini moab.
Theres a number of roads through the Oquirrh mountains that explore old mining areas. Don't know many details.
Have fun, do some more research and be respectful of private property and the wilderness so as to stay outta trouble. People can get real angry these days when you screw around off trail and leave trash etc.
Heres a book I recommend. There are a few near the valley listed in it with trail info and more. http://www.amazon.com/Utah-Byways-Utahs-Backcountry-Drives/dp/0899974244
EDIT: Oh yeah! I almost forgot there are a couple great trails up American fork canyon but they are moderate to technical. Great scenery! Take a friend with a four wheel drive, its necessary. And make sure you read up on them. Like I said they are pretty technical.
I recommend that you get a copy of Tony Huegel’s Utah Byways .
Also, I bet you will enjoy the White Rim Trail in Canyonlands NP.