Arches National Park is located a few miles outside of Moab, Utah. The best time to visit this park is in early spring and early fall, as it gets really hot down there.
There are areas where you can have a picnic and enjoy some amazing views. You can hike up to the delicate arch, but I do recommend that you have tons of water and a camera. It is a long hike about two to three hours.
There is also a broken arch that is interesting to see. There are also tons of lizards hiding and playing on the rocks. Plus there are rabbits around to, though they are still really skittish of people. Whereas the lizards don't seem to be unless you try to pick them up, then they run.
There is also a slot canyon that you can walk into and it opens up into a little clearing of sand. It is a great place to have your kids play and rest for a few minutes.