There are no sites in Yellowstone that have electricity except Fishing Bridge. That campground was closed this year for improvements and when it is open, is only for hard sided units. There are campgrounds available outside the Park that have hookups (West Yellowstone, Gardiner, Cody) but Yellowstone is a big Park and you will be driving a lot. https://www.nps.gov/yell/planyourvisit/campgrounds.htm
I highly recommend staying inside the Parks if you can. You can avoid some of the traffic by getting up early and being back at your campsite by mid-afternoon. I've stayed at Grant Village multiple times and have enjoyed it. You are close to the lake and have showers, restrooms, etc. close by. Start planning now as campgrounds book early in these Parks.
We stayed at Yellowstone Valley Inn CG near Cody in the Wapiti Valley. It had hookups and was a very nice place. But it caused us to drive A LOT just to see the park.
If I did it over, I would try to stay in the park. It would have been worth the pack up and un pack to move once or twice. I think Canyon takes reservations.
* Don’t miss the Beartooth Highway. It’s worth it.
Bridge Bay, Canyon, Fishing Bridge, Grant and Madison all take reservations. All are dry camping. There are several other campgrounds in the park that are first-come-first-serve.
We stayed in West Yellowstone, MT when we went. Our campground was five minutes from the West Entrance station, but about 25 miles to Madison Junction. Didn't matter though. It's a really nice drive that we didn't tire of.
No matter where you stay, if you want to see the park you're going to log some miles.
As crackerJack said, don't miss the Beartooth Highway. It's incredible.
There are at least 10 specific YS threads that go through all the camping options with recommendations. Can be found by searching for Yellowstone. In addition, the NPS has a pretty good site on the park and there is a whole section on camping.