I say stay in the park! Nothing better than waking up and you are right in the middle of Yellowstone!
We stayed at Bridge Bay in a Class c and really enjoyed it. We tow a motorcycle and did most of our touring with that, but did use the rv for touring twice. The first, we were meeting a ranger for an early morning hike; we arrived early to be sure to get parking, then cooked breakfast. We sat in the RV with a nice cup of hot coffee until the ranger arrived. The 2nd time, we went to Hayden Valley to look for wildlife at dusk; cooked dinner in the RV! So, there are perks too as you will save money having your food and drink right there. Also, you won't be alone; there are a lot of renters out there who don't have any other option. If you are going to an area with limited parking, just be sure to leave early in the morning; which you should do anyway for a better chance of seeing wildlife and avoiding the crowds (at least for a couple of hours).
On our upcoming trip, we are staying at Canyon. Can't wait! Have a great trip!