I'd also recommend making the reservations at Madison Campground. It's about as well centered as any. In fact, if you need hookups I'd point to West Yellowstone (or further), which is another ~20 miles west of Madison.
As others have said, start out early in the morning. I used to visit several times each year, and we'd be out of camp before sunrise, then back in camp at 10 or 11 a.m. until 3-4 p.m., then back out until dark. We were concentrating on photography, and the best photos usually are found in early morning and late afternoon. Just so happens that's also the best time to avoid the mid-day crowds/traffic. :)
