As mentioned, make the reservations for the NPs, but give yourself a few extra days in between,so you don't feel like you are rushed.
Getting to a CG within a half-day of Yellowstone, will allow you to be relaxed and not worry for that last days drive.
Plan for the unexpected! Better to be there a day early, and spend the night at a Walmart, than to be rushing all day because you had a blown tire.
Sometimes, it's nice to set up your trip to camp about a half-hour from the sights. Most folks will want to be as close as possible, and those places will be packed. Get a bit outside the loop, and you may have more success.....and you can camp the night before, then get an early rise to view the sights...then head back to the CG to relax for that night.