I been there 6 times and here is the way we do it. Coming from SoCal we spend 3 days in West Yellowstone at Grizzly RV park to tour the west and northern part of the park. Then we move on to Fishing Bridge for 4 or 5 days. Then on to Coulter Bay campground for 3 or 4 days to tour the Teton area.
Yellowstone is a huge area and to minimize driving time is the reason we move to different area's. What ever you do don't rush your visit if possible. There's so much to see and do, especially with viewing the wildlife. We are pretty much gone for 12 hours each day and then return to the camper.
Reservations need to be made ASAP, especially at Fishing Bridge. If you go later in August or early Sept. your chances are better getting a reservation.
If this is your 1st time to the parks, study maps, brochures, websites to get an idea of what to do. It's our favorite place to visit. Enjoy your vacation. You won't be disappointed.
Wireman