yellowstone grand tetons without reservations

Since you know the approximate total mileage to get there, and how far you want to drive per day, you can calculate when you'd get to Yellowstone. Add a day, perhaps, for delays or extra sightseeing enroute, and make your reservations to start then. August is still busy in the park; attendance doesn't drop off like a rock until perhaps mid-October, so even after most schools start, visitor numbers just decline very gradually. The first-come, first-served CGs inside and outside the park will mostly still fill up each day, so you would need to show up by mid-morning to find a site (even then, not guaranteed.)