Check out Moab, only 3.5 hours from SLC. You can easily visit Canyonlands & Arches National Parks if Moab is your home base! Great off-roading, mountain biking, and hiking near by as well. Highly recommend hiking Fisher Towers, Corona Arch, & Grand Staff Canyon Reach out to Paige if you're looking for a good camping spot and for other recommended hikes!
Paige's second all-time favorite National Park. HIGHLY recommend the White Rim Road if you rent a high clearance vehicle. You can do the entire 100 mile drive in a day but bring extra gas! You can also do an out and back. I recommend starting at Shafer. Day use permits can be obtained the day before. Reach out to Paige for more details! Otherwise, visit the Isle In The Sky section of Canyonlands for a bird's eye view of this massive and impressive canyon.
The least visited of the Mighty Five Utah National Parks but this park does not disappoint. Highly recommend renting an off-road vehicle and driving the 75 mile Cathedral Valley loop. No permit required but this is very remote so please come prepared!
Paige's favorite National Park of all time. Highly recommend renting gear to hike The Narrows from bottom up, out & back (no permit required). Or scoring a permit to hike the infamous Angel's Landing. This park is rather crowded and requires a shuttle bus to access the canyon. Wake-up early and catch the first shuttle bus to avoid the crowds!
Bryce Canyon National Park is located about an hour from Zion. Highly recommend this out of this world park. Numerous amazing hikes through hoodoos and other interesting land features. You honestly can't go wrong with any of the trails here but I personally recommend Navajo Loop, Queen's Garden, Peekaboo and Wall Street (which all of these can be combined).