We spent nine days at Fishing Bridge last month. If you're planning a trip next year, make your reservations now. Staying in West Yellowstone will be quite a drive. Even staying at Fishing Bridge, we averaged 133 miles per day. And the max speed in the park is 45mph. I would do Grand Teton last before heading to RMNP. You'll have to go through it anyway to head south. Plus it will give you a chance to see Jackson, WY. When you leave, I would go through Moran. Jackson is very tight with heavy traffic. We came through there on our way into the park. White knuckled the whole way and forced to go straight through the middle of town. Not sure how many mirrors I took off of parked cars.
We took a day and went to West Yellowstone. If you like high priced tourist traps with not much in the way of restaurants, it's ok. Ate at one place and paid $15 for a dried out burger. Not really worth the hour + drive. The campgrounds there were large with all the amenities. But absolutely no trees. The best part of Fishing Bridge was being in the tall pines and the fresh pine smell in the morning. But these are just my opinions.
If I had to do it all over again, I'd stay at Colter Bay campground in Grand Teton and drive into the park from there. Lots more room and pull throughs at Colter Bay. And you're not far from Jackson if you want shopping.
TV: 2012 F250 CC SB SRW 6.7L Diesel w/air lift suspension
CHU: 2012 Keystone Montana 3750FL
Hitch: B&W Turnover Ball w/ Companion 3500
Family: Me, HH6, a Boston Terrier, a Shiba Inu