We were there in May and drove all the main roads. As stated Old Faithful has a lot of parking within 1/4 mile or so. The only difficulty I can see with a large RV is limited places where you may want to make a U-Turn. Even that shouldn't be a big problem.
The main roads form a figure "8" and there was some construction on the northwest section. In another area the road washed away so we had to drive a lot of extra miles to get back to campsite. I'd expect it's been repaired by now. We stayed at Fishing Bridge campground where we had stayed in the past. It's centrally located for what we wanted to see and had electricity which we need.
Yellowstone is a great place. Hope you enjoy.