We LOVED Farragut State park when we stayed there. It's about 30 miles north of where you're currently looking though, so rather than burden you with details, here's a link to more info:
Farragut State Park
Just lots to do there and gorgeous private sites. (We got temporarily lost playing on one of the disk golf courses that they have available! :) ) Perhaps a bit out of your way though.
We've been there a number of times. We've always felt that some of the bigger campgrounds, such as Madison or Grant tended to have a "refuge camp" feel about them that just was too packed together for us. Just a personal preference thing though. Canyon is a larger camp and does have lots of fairly private sites.
Our preference has usually been Norris, which is centrally located, and Lewis lake, but Lewis is positioned more to the South. Some of the sites in these camps just seemed more private than the bigger camps. If you're coming from the Teton direction you could check out Lewis lake on the way into Yellowstone.
Last trip we stayed at Lake Hebgen but that is well outside the Western boundary of the park. Very nice and private sites though. There are quite a few camps just outside the Eastern boundary as well.
If ya go the generator route? Just try and be considerate! There was one camper at Norris that ran his loud generator so often and for so long that whenever he turned it off the whole campground would cheer! Literally! We boondock quite often -- I've got two batteries and a small solar panel and make it a week off the grid easy, but granted, no TV running or anything. Water pump and furnace fan are the big power consumers but we easily make a week.
Have fun ... it is gorgeous!