Grand Canyon Railway RV park is a Passport America park and you can get that half price rate off season if you are a member. Its right at the Station to catch the train to the South Rim and they have a great Buffet restaurant there. The RV park is very nice I thought with clean facilities. They may still be offering use of the hotels swimming pool and exercise room.
Williams is a good place to base from and town has some nice shops and good restaurrants. Rt. 66 has been replaced for the most part by I-40 but there are still many parts that you can drive and still parralell I-40. Towns on the old 66 are pretty much ghost towns as the interstate has hurt them.
If you are planning this trip for like within the next couple of weeks then be ready for cold weather camping. The Grand Canyon Plateau is 66oo ft. elevation. Weather shows highs in the mid 50's with lows in the low to mid 20's.