Dan,
It is good to worry about theft but the Moab area and the southwest in general is pretty safe, in my opinion. I've photographed the Colorado plateau since 1995, including Moab numerous times and the only official police warnings I have heard were, and still are, at Canyon De Chelly.
With that said I always keep my gear stowed in black bags and never laying out for people to see, except when using it, of course.
There is a candy store of treats to shoot near Moab. Arches of course, Delicate Arch (afternoon), but also Canyonlands Island in the Sky, Mesa Arch(sunrise), Dead Horse State Park overlook (either), Fisher Towers area (afternoon). Just south of Moab is Tukuhnikavits Arch, (afternoon), short hike involved.
Driving from Moab to Yellowstone is a slog with nothing to shoot without a diversion of more than a few miles. Be sure and go through the Tetons.
Best,