There are campgrounds in the Mt Rainier park itself, but when I last looked they did not have sites big enough to take our rig (36'). We stay at Alder Lake (
http://www.mytpu.org/tacomapower/par...rk/Default.htm). Its run by Tacoma Power, but can be reserved through the same system used by the Washington State Parks system. Its a good price with a mixture of back-in and pull-through sites. Some have full-hook up and some are water and power only. Its next to Alder Lake (which has a boat launch too if you are interested). From Alder Lake expect to drive for about 1 hr to get to Paradise on Mt Rainier (most awesome place especially when the clouds stay away).
Hope this helps.