There's always Canyonlands up the road (or down the road too) and Dead Horse Point.
yep, still plenty of beautiful places to shoot. and it sounds like a couple of days a week arches is still doable at sunset/sunrise, although I think I read they were going to put some restrictions on night shooting at some of the locations.
My favorite place to shoot sunset is Green River Overlook in Canyonlands, with Grand View a close second. Get there early, find a nice quite place to eat a sandwich. About as peaceful and breathtaking as it gets. Dead Horse Point is fantastic at sunrise, and of course everyone knows about Mesa arch. Also if you are in for a little hike, False Kiva trail starts a little past green river overlook turnout.
And you can head up out of town along the colorado and get some good stuff including Fischer towers, or over into the LaSalles. On the way from Moab to Monument Valley it's pretty easy to hit "House on Fire" ruin, easy hike, best time to shoot it around 10 or so in the morning.
That's just for starters if you are headed through Moab