We have made this exact trip about 10 times in the past few years, last few in a 40 footer.
Road is good and the area is simply breathtaking.
Do you have reservations at all?
Here is my suggestion based on our experience. Do not stay at The Virginian RV in Jackson, its overpriced and crowded. If you are up for dry camping (no hook-ups) I would stay at Colter Bay Campground in Grand Teton National Park. It has loops for riggs your size and also allows generator use 8 to 8. Campground is well laid out and you cannot beat the area.
If you look at your map and that is too far out for you I would consider Gros Ventre Campground just north of Jackson about 12 miles or so. Its another NP campground We have stayed there in a 40 footer, its a little tight but worked.
For a few nights and if you want hook ups there is a RV park at Colter Bay we have not stayed there, however its gotten great reviews. Would highly suggest making reservations or seeing if they have any spots.
great site is www.rvparkreviews.com
click on state then area, great site, gives info and also websites and you can find phone numbers there also.
Now as far as West yellowstone, would highly recommend Grizzly RV in West Yellowstone. Stayed there last Oct for 10 days and high recommend calling for reservations. They have back in, pulls thrus etc...very nice campground and people.
Cannot beat the location, walking distance to town and shops and so close to the West entrance to Yellowstone itself. We have made that our "base" and traveled into the park daily from there.
Another great travel resource is a book called Mountain Passes of the West, gives all kinds of info on mountain roads and grades, so if you have concerns or will be traveling in the west a lot gives you good info for planning what road you want to take or not.
Campground at Colter Bay is first come first serve, but if you get there early in the day, like before 1pm or so you should get a good spot. They have picnic tables and fire rings, also a dump station.
Colter Bay itself is intersting, little store, gift shop and two fairly good places to eat.
We are going back (again) for three weeks this September. Love the area and cannot get enough of both parks.
Hope this info helps...
One more thing. If you travel with a laptop and are looking for wifi hook up, also if you are in a tow vehicle, visit Jackson Lake Lodge. Visit it for more reasons that a wifi hook up the view alone at the top of the stair case will cause to you stop in your tracks! however take your laptop upstairs, there are plug ins so your battery does not go low and free wifi. Gives you a chance to catch up with things should you need to. I generally sit on the hearth by the big fireplace.