If you are talking about the Island in the sky district, your choices are limited. It's going to depend upon what you mean by "big rig". The camping down on White Rim is very primitive and you wouldn't get any MH down Schaefer trail into that area. That area is best served by SUVs and tents. Up top, Dead Horse Point State Park is your best bet. A 30' MH I could see. A 35' coach I doubt. And, there are no hookups. I'm not familiar with the Needles District. We'll be staying in Moab at Portal this June and taking the Jeep into the various areas. Moab is close and there are a number of full hookup campgrounds that are truly big rig friendly.
Mark & Leann Quasius
2016 Cornerstone 45A
2007 Allegro Bus 42QRP (Sold)
2012 Jeep Wrangler Unlimited - Rubicon