Slickrock Campground would probably be fine. I was there two weeks ago to do some 4 wheeling in the Jeep... Seemed like there were quite a few bikes running around without plates. I think if only one bike isn't plated, put him/her in the middle of the group to kind of camouflage the fact the bike isn't plated.
Hit fins n' things. It's the quintessential Moab trail. It will get you into the mindset of the obstacles, traction, and angles you'll be dealing with while you're out there.
BLM land is all good.
The national parks require plates for the trails within them. So if you're planning on riding to eye of the whale or tower arch or go down south to the needles to run elephant hill to hike to the convergence of the Colorado and Green rivers that one bike will be out of luck..
Have fun, take extra water, and be safe.