Stay anywhere you want - BUT - my advice is to do it later in the season September is HOT. For the most part we never make reservations and really know little or care much about the Camp Grounds - we come to see the Canyons - River - Arches - and the people - so staying in any Cg is just fine for us.
If you are able to plan, IMHO September is the time to be in the Rockies - November in Utah (OK late October and all Winter) - and I would be remiss to not make that point.
Best of luck,