Dead Horse Point State Park
Dead horse point is famous for it's amazing views overlooking the Colorado River. This park is close to Canyonlands and next to a bunch of mountain bike trials and jeep trails (see the Mag 7 and Gemini Bridges area). Camping here is often full during the peak times of the year, so plan accordingly. If you're into mountain biking, I high recommend the trails in the Magnificent & area. They have some of my favorite all time single-track trails in Moab.
Goblin Valley State Park
If you're coming to Moab from the northern part of the state, odds are you'll pass close to goblin valley. Famous for its unique rock formations. There are some campgrounds here, but it's also great to see in a short visit as you're passing by.
Goosenecks State Park
If you're coming to Moab from the south, check out Goosenecks State Park. A small park with impressive views that overlooks the San Juan River.
Green River State Park
Catch the Green River State Park during the annual festival of Green River Melon Days. Green River is famous for its delicious watermelon which can be purchased during the summer months in Green River, Moab, and surrounding areas.