There are far too many iconic places to list for Moab/Canyonlands area.
Just before you get to Canyonlands, take the turnoff to Dead Horse Point. This is a Utah state park and $10 entrance fee is required, but it is a spectacular vista rivaling Grand Canyon IMHO. Good for sunrise and early morning for one side, late afternoon / sunset for the other side. I prefer mornings.
At Canyonlands:
The overlook opposite the visitor centre is very worthwhile, as are the canyon viewpoints along the road. Mid-afternoon works best IMHO, before shadows start encroaching.
Green River Overlook is another fantastic vista, great for sunrise and late afternoon.
False Kiva is a great photographic location, although it is not on any maps. Google for images, then ask at the visitor centre and they will give you instructions on how to find and navigate the trail. I did this on the weekend and had no problems. It's very hard to shoot because of the combination of dark shadow and bright light. Sometime mid-afternoon when the kiva is lit up (between 2:00 pm and 5:00pm), or about sunset (8:00pm) might be the best times.
Mesa Arch at sunrise is the iconic Canyonlands shot, although there will be lots of photographers as summer draws near and yo need to get there about one hour before sunrise to grab a spot.
You might also want to consider heading up to Green River then down Highway 24 to Goblin Valley State Park. Close by is Little Wild Horse Canyon, which is a nice slot canyon hike (about 8 miles) so do that earlier in the day followed by Goblin Valley around sunset.
If you are in a 4WD then you might want to think about Schaffer Trail or White Rim Road, although both are very rough and progress may be slow. There's probably no campsites available so plan for short day trips only.
At Arches:
Full of great locations, although it will be getting very crowded at that time of year.
Delicate Arch at sunset is the iconic shot, although shadows may be a problem. Winter is best for sunset, so plan on getting there early (about 3-4 hours before sunset) to get a good shot of the arch and its bowl before the crowds and the shadows get in the way. However you won't get the best colour until sunset.
I like an early morning hike to Landscape Arch followed by a hike to Double-O arch. Landscape Arch looks best at sunrise/early morning. The hike to Double-O is spectacular, as you need to climb along fins of rock that show amazing vistas to the north. Best shot of Double-O is obtained by walking through to the other side and up the hill a bit.
The first amazing sight at Arches is Park Avenue, which works best early morning/late afternoon. Bring a wide-angle lens to get the best shot. Don't forget to look to the upper left for Queen Nerfiti's Head rock formation. There's a nice shot if you climb up a ridge a bit to frame a pinion pine leading up to Queen Nerfititi. I would recommend hiking through Park Avenue to end up at Courthouse Towers (although you will then need to hike back).
The Courthouse Towers, especially The Organ, are amazing. There's an iconic shot of looking up towards the Organ, with wildflowers in the foreground. Great for sunrise and later afternoons.
Balanced Rock: great for sunsets as the colours change. You can also cross the road and stand on some rock formations to get great silhouettes at sunrise/sunset.
The Windows: North and South window are best shot late afternoons. You can also walk through North Window, climb a rock on the other side, to get Turret Arch framed within the window. This is another iconic shot and is best at sunrise. Double Arch is a short walk and is best shot in late afternoon IMHO.
I would also recommend a ranger-guided walk through Fiery Furnaces. You will need to book in advance for this (not sure if there are spots left) or try your luck on the day by asking at the visitor center.
Sand Dune Arch has some great light and textures, since it is inside some rock fin formations.
In a 4WD you can do the Salt Valley road to get to Tower Arch, etc. Should be fun.
Around Moab:
Take the Potash Road and head to the spectacular Corona Arch. One of my favourites, best photographed in the late afternoon IMHO (although you could also shoot it from the other side in early morning). There's some great scenery along Potash Road as it follows the Colorado River. Some sides will look best early morning, others in late afternoon. There's a 4WD track at the end of Potash Rd that leads to the other side of Dead Horse Point. I haven't been there but it should look amazing.
Conversely, head along Highway 128 to follow the Colorado River eastwards. You can hike Negro Bill Canyon, and see Castle Valley and Fisher Towers. Best to get to Fisher Towers mid-to-late afternoon and do a hike around the back. Then head futher east on 128 to find a bend in the river that allows a great sunset shot of the Towers and their reflection.
About 25 miles south of Moab there's Wilson Arch (right off the road) and then you can head into the Needles district of Canyonlands.
Actually you should just get Photographing The Southwest Vol. 1 by Martres and read the section on Moab/Canyonlands.