Ahhh...I love Moab, it's my hometown. I haven't lived there for a long time but I go back to visit often. The road riding there is great and underrated IMO. The only thing is you have to plan longer routes carefully since you're kind of out in the middle of the desert.

Moab is small and it's the only populated area for quite a distance in any direction, so be aware that once outside the city you aren't going to find much in the way of rest stops. Make sure you know if there will be anywhere available to get food/water along your planned route, and bring ample food & water supplies to get you there. And make sure you've got tools, tubes, etc. to support yourself in the event of a flat or mechanical issue.

Larger roads like the main highway (192) have ample shoulders. I wouldn't call them "high traffic" because it's a low population density, but it's a truck route and high speed limit. It may be unnerving if you are not used to the speed differential; but if you are then you probably won't mind because it's lower volume of traffic if that makes sense.

The Nat'l park roads through Arches & Canyonlands will give you some spectacular scenery, and the Arches road starts out with a nice little climb. You'll want to be careful of traffic there and wear your high-visibility clothing, because the roads often have narrow shoulders and sometimes people are busy looking at the rock formations rather than at the road.

You said you were looking for some 40-50 mile routes with hills...if you're up for a challenge you might look at that 2nd link that out spok'n included in her post, which includes route maps for the Moab Century tour. The "Big Nasty" hillclimb up into the San Juans is pretty epic and is very light on traffic. You could do the climb and then turn around & roll back down for about a 50'ish mile ride, or continue on down the other side and do the 65 mile loop as noted in the map. (Note: make sure your brake pads have some life left and that your brakes are in good working order if you do this route - the descent is steep and windy, but a lot of fun! And watch for gravel if you go down the backside.)

Check the forecast before you ride. Moab can get very, very hot in the midday sun (though you'll probably be OK in May), and it can also experience fast-moving desert thunderstorms.

If you have a camera that you can fit in your jersey pocket, bring it. There are lots of good photo opportunites in the area. Have a good trip and then come post all about it!