Another option is to say at Colter Bay just south of Yellowstone. You will be camping at one of the most scenic spots in the World. Walk a very short distance and you get a view over Jackson Lake and see the Tetons. We have also stayed in West Yellowstone. It is packed in summer. But you are very close to Henry's Lake and can take the drive up the Madison River towards Ennis. If you go there you will want to get up EARLY and get into Yellowstone as early as you can. If you choose the Gardner area you will be in one of the nicest valley's in the USA. A number of the rich and famous own big ranches there. There are a couple of RV parks a bit north of Gardiner in Paradise Valley that are right on the river and have a really beautiful setting.
If you have a 40' or under RV Fishing Bridge is the best option. Or going RV-less and staying at one of the classic old lodges. We love Yellowstone Lake Lodge. And if you can get in the Old Faithful Inn is awesome.
My pick would be Colter Bay unless you have to make a drive into Montana. Then pick between the other two.