Arches National Park
We have spent LOTS of time in Arches! Arches is a neat place to explore. If you're camping, the National Park Campgound, Devil's Garden Campground, is amazing. The sites are fairly large and private and interesting. And, it is a small campground. You MUST make reservations in advance. You will love it. Check the website for details. The campground is at the very end of the park which is one way in, one way out. So, make sure you are equipped before you head back to the campground for the night.
Arches is an awesome place for dayhiking! There are many dayhikes that are very accessible. You can drive up to the trailheads and each trail is full of outstanding sights. One of our favorites is Delicate Arch, the hike all the way up. Best time is dawn or dusk. It can be very crowded at sunset so if you don't want big crowds, go early. We have always wanted to do the Fiery Furnace which is Ranger led. You need to make reservations.
FINALLY: However, heed if it is HOT, we would not recommend camping out unless you plan to be busy during the day or staying in the shade and cool. There are no electric sites. Kids, especially, can get quite cranky in the heat of the day when it is over 95. When we have gone during these months/heat spells, we have stayed in a rental. You can usually find a decent rental house so you can be in AC! As far as being active, we get out hiking EARLY, then spend the heat of the day doing inside things in town, taking a rest, going to the town pool, or finding a watering hole (there is a great one just out of town!). In the evening, we get back out on the trails.
The town of Moab is chock-full of things to do. For extra adventure, you can do water activities on the river, go ziplining, go on a jeep tour, take a self-directed trip to see petroglyphs. There are lots of outfitters/businesses to employ!