I stayed at GB NP about two years ago. It is one of the least developed NPs so your accommodations will be modest. The Upper Wheeler campground is gorgeous but impossible for a class A. The sites are too small, the road narrow and steep.
I believe we stayed at the upper Lehman CG. There were a number of sites that could take a big rig. Here is the site map: http://www.nps.gov/grba/planyourvisi...20Lehman-2.pdf
The lower Lehman seemed even more accommodating of big rigs; however, it was much less scenic and seemed much hotter.
No reservations here. I'd recommend arriving before Friday as it seemed that the weekends really filled up.
There is a dump station with potable water near the main entrance. Don't forget the cave tour. I really enjoyed it.
I also think there is a very rustic RV park in Baker. We fueled there and I was glad we stayed in the NP.