Moab, Arches National Park, Canyonlands National Park, and White Wash Sand Dunes
Moab is only a 3.5 hour drive from SLC, so you can easily spend a weekend there! It's beautiful! The red rock will take your breath away if you haven't ever seen anything like it. I would highly recommend going on a trip there before you leave Utah.
Arches National Park is 10 minutes from Moab and Canyonlands National Park is within a half hour. You've got to visit both when you're in Moab. If I remember right, it's about 25$ to get a car into the park. Every once and a while, they have free days where you can enter without any charge. You can follow the free days on this website https://www.nps.gov/planyourvisit/fee-free-parks.htm. The downside to this is that the parks are usually very busy on these days.
Canyonlands has a great scenic drive, as does Arches.
The famous delicate arch is located in Arches National Park. Although you can't see the arch from the road, you can hike to the arch and stand below it. It is a 3 mile hike and is mostly uphill, but it's well worth the hike. I would recommend going in the Spring or Fall because summer months can be extremely hot and winter months can cause the trail to be slippery from ice.
White Wash Sand Dunes has a huge area of land covered with sand. It is about an hour drive from moab. It's fun to get an ATV and play around. You can rent 4 wheelers, and side by sides in Moab.
