I have been through the area on this loop several times, and can't wait to get back there this summer.
We have twice stayed in Page AZ at the Page RV park on Coppermine Rd.
From there it is 145 miles to both the North Rim and South Rim. In the long days of Summer, getting up early and staying out until dark and driving back in makes for a long day, but a day trip is doable IF you don't mind a long day. The north Rim is usually open by May 15. There is a campground at Jacob Lake which you should check out if you don't want as long a day trip.
Once in Moab, if you want to see one of the miracles of Canyonlands, get up EARLY, about 2 hours before sun up, and drive out to Mesa Arch overlook, and watch the sunrise.
This is your reward:
This photo I took and is in my office printed at 20" x 47".
There is a lifetime of travel in the Grand Circle. You can't see it all in one trip.