We have been going to Arches National Park almost every year since we met, it's a wonderful place and we recommend seeing it. Arches offers a beautiful drive throughout the park, as well as many short and long hikes to do.
Please note- a few of the more popular National Parks have moved to a reservation based system. Please visit their website to obtain a reservation. Alternatively, you can visit the park prior to 7AM, or after 4PM without a reservation.
Another beautiful National Park within driving distance of Moab. The park consists of 527 square miles of colorful landscape that has eroded into countless canyons, mesas, arches, and buttes by the Colorado River.
Reservations are not required for Canyonlands National Park.
The Colorado River runs through Moab, and there are many areas you can hang out on the beaches of the Colorado off of UT-128.
This is probably where you'll find us :)
Moab Adventure Center offers a ton of great things to do local to Moab. Take a speed boat down the Colorado River, a sunset dinner cruise down the Colorado River, off-roading, rock climbing, canyoneering, etc.