We drove 26/287 from Lander to Jackson Hole back on May 30th. As already mentioned, it's a gradual climb. The descent is a bit steeper, but not bad at all. Lots of snow on the way up to the pass when we went through. Both Brooks Lake and Falls Forest Service campgrounds were still in accessible due to snow.
Also an X2 on Gros Ventre campground. We spent 9-10 nights there during the last two weeks of June this year.
If you can survive without FHU, there's Baker's Hole campground just 3 miles north of West Yellowstone. They had some electric sites. There's also Henry's lake State park some 15 miles or so west. Not sure whether they have electric sites. Red Rock RV Park, also near the lake, has hookups.