Just to add to the confusion, here's my 2 cents:
If we were to stay in only one campground for Yellowstone, it would be Madison. Sites can be reserved, generators are allowed (8:00AM to 8:00PM) and it is centrally located, especially for the thermal features, which are mainly between the Old Faithful area and Norris. From Norris it's only 12 miles to the Yellowstone Canyon and the water falls.
My second choice would be Canyon campground, if Madison wasn't available.
IMO Fishing Bridge and Bridge Bay add unnecessary time driving to what is already your limited time in the Park.
Flagg Ranch is too far away and Colter Bay, which is great for Grand Teton NP, is way too far. If you possibly can go to Grand Teton after Yellowstone. Some of the most spectacular mountain scenery in the country.
Get an early start on the day you plan to drive the Chief Joseph and Beartooth Highways. That's a long drive and you will want to stop to enjoy the scenery. Also you will pass through the Lamar Valley in the northeast corner of the Park on the way. The valley is called the "Serengeti of America" and contains the largest herd of Bison in the Park. We got lucky and saw five wolves there last year.
Also plan for a full day at the Old Faithful, Black Sand Basin and Biscuit Basin thermal areas. Something like 25% of the geysers in the world in this area. Have lunch or dinner at the Old Faithful Inn.
