We've always found Madison campground to be about the most convenient for MOST of the park. The park is larger than some states so the most CENTRALLY located would depend on what type of things you value the most. Madison is convenient for geysers and fumaroles plus lots of other scenic areas like Fire Hole River area. If you plan on spending most of your time in the Northeast part of the park (best for wildlife viewing and visiting the Canyon area) then the Canyon campground would be a good choice. If you feel you must have full hook ups then be prepared for parking lot like camping only. A better option would be just outside of the park at West Yellowstone. Camping is cheaper, MANY more choices and in some cases a much more "camping like" experience. You WOULD make it more inconvenient to attend the myriad of GREAT campfire / Ranger presentations available at most inside the park campground. There are also several really nice COE / NFS campgrounds located only a couple of miles north of West Yellowstone. Very convenient to visit other area attractions like "Quake Lake' which is the site of the huge earthquake of some 60 years ago.
Good luck and have a great trip / Skip