Likely the best place to ask your question is at Yellowstone Net (
http://forums.yellowstone.net/). Lots of Yellowstone and Grand Teton nuts over there, including me.
One thing to know about Yellowstone is it is BIG!!! Many miles from place to place and 45MPH is the maximum speed limit. Some areas are marked slower. Furthermore there will be critter jams here and there around the park where it may take 30 minutes to as much as and hour or more to get past them. They will add time to travel times. I'm now of the opinion to stay in the park. With the prices of gas, you will save more than the additional cost of the higher campground fees. Reserve the first night or two at one of the reservable campgrounds. The look for a place at the campground you really want after you get there. yeah, the campgrounds will be full and crowded in the summer, but that is life. how much time will you be spending at them.
For best animal watching, get up before dawn, and go out so you are out there at dawn and sunset when the temperatures are cooler. Most of the animals will bed down and sleep during the mid day. I do the same, or I photograph stuff that isn't going to be washed out by the stronger mid day light.
BTW, on the east side, very close to Yellowstone is a distributed camping area along one of the side roads.
PS, if you do want to stay in the park, GET YOUR RESERVATIONS IN EARLY!!! They fill up fast. They need to double or triple the amount of campsites in the park. They could stand to do the same with the hotel rooms too. The environmentalists would flip over either.