So how many days will you have in Yellowstone?
As others mentioned, the only campground with full hookups INSIDE Yellowstone is Fishing Creek. But it has more of a parking lot feel than campground. Some folks have posted that they spent so much time in the park (vs. time spent at campsite) that they didn't care, but I wanted a camping experience. So we stayed at Canyon Village. It is a GREAT campground but NO hookups, not even electricity. There are public rest areas to use and wash dishes, and a dump station at the exit. And by switching to LEDs we survived 5 nights on a single 12V battery.
Norris and Madison campgrounds looked excellent too. But it may be too late for reserving a multi-night stay this summer. Check out this link.
http://www.nps.gov/yell/planyourvisi...ellowstone.htm
Here's another idea: if you want a campground with full hookups, consider Colter Bay in Grand Tetons NP. It is only ~30 minutes from the southern entrance to Yellowstone. And it is a good campground. I would stay there vs. a commercial campground outside of the parks.
Here's a link to Colter Bay RV Park:
http://www.gtlc.com/lodging/colter-b...e-rv-park.aspx
My family had a blast at Yellowstone and Grand Tetons last year.
John