Yeah its not Utah. I just googled "closed dirt road" for an image. >>1255512>Also where do you go out in Utah? SLC friend here who doesn't know where to go.
I am in Utah county. Timp is always fun but way too crowded. The desert out by Genola is good for rabbits. I live right next to Hobble Creek Canyon, so I like to camp down the Right Fork. Nebo is a good hike and doesn't have the crowds. I really like the Uintas (do Kings if you haven't yet - best hike I have been on. It's a 3.5 hour drive from SLC) I try to get out to the Unitas once or twice a year.
I don't know much about SLC trails, but Timp is definitely worth the drive (it'll only take you 1:15). You'll have to wait until mid-July to get up there with no snow. Go do Kings Peak or Red Castle in the Uintas.
If you're looking to car camp, there's some beautiful country on Squaw Peak Trail - just take your 4x4. Roads will probably open on Memorial day. If you don't have the wheels for it, there's always Hobble Creek Canyon. Take the right fork and drive the dirt road until you see something you like. Right fork was closed last week but should open soon, it isn't super high elevation. You have to get like 10 miles in before they let you stay in unmarked sites, but it's worth the drive. You can be totally alone for a week if you hike into the brush a quarter mile.