The last 2 visits to Yellowstone was in July (2010) & Aug (2009). We stayed at Mammoth CG in 2009 & Grant CG in 2010. We have been 4 times all together & never had a reservation. Madison, Canyon, Bridge Bay as well as Grant & Mammoth CGs all should be places to consider. However, you would have to check the park web site to make sure about the 40' rig. Mammoth has some site which would work. There were really large rigs there.
South entrance via the Tetons is the easiest route into as is the North entrance by Mammoth. West entrance would be easy enough, but take a lot more driving to get around to it. East entrances one will have to do some climbing.
Here's an older post with info from our past trips, etc.
DesertHawk's Recommendations for Yellowstone Area.