Moab is a great base for exploring Arches, Canyonlands and Dead Horse Parks. There are many accommodations in town and it's a center for mountain biking and many other outdoor activities.
The best places to eat in town are the Desert Bistro and Moab Burger.
Local photographer Tom Till runs a gallery in town https://tomtill.com
Arches National Park
Fiery Furnace hike is one to do must needs to be booked well in advance as it is popular.
Turret Arch is an early morning destination to get the classic arch within an arch image. Walk through the arch and behind it for the famous view.
Another short and easy hike worth doing is Landscape Arch, the longest arch in the world.
Finally no visit to the park is complete without watching the sunset from the viewpoint over Delicate Arch, the most famous one in the park.
Canyonlands National Park
Another quick drive to reach from Moab.
Mesa Arch is a short hike to the most famous site to photograph here, but to take the classic sunrise shot requires getting up well before sunrise in order to stake out a spot near the relatively small arch. It's worth visiting any time of day however.
The other must do hike in Canyonlands is the one to False Kiva. It's not a long hike but it can be a little tricky to find the alcove. It's best done in the late afternoon from a photographic standpoint. See my blog post for more info on this one.
Dead Horse Point State Park
While in the area one other place well worth visiting is Dead Horse Point State Park. From the overlook here you get a fantastic view of the Colorado River valley below, before it forms the Grand Canyon proper.