Some good advice so far; time spent at the various locations is a subjective thing. We spent a week in the Black Hills, still didn't do & see everything we wanted to, and felt it was one of our best camping vacations ever! I could spend a whole day at Crazy Horse, though 2 hours seems about right for Mt. Rushmore. :) Lots of good choices for camping in the Hills; search this forum for "Mt Rushmore" or "Black Hills" and you'll find a lot of recommendations. Custer SP was mentioned, and it's quite nice. Also lots of recommendations for YNP CGs on this forum as well.
I would NEVER consider trying to camp in/near Yellowstone & the Tetons in the summertime without reservations. There was a good point made about having a generator - if so, you could perhaps get into one of the first-come, first-served CGs, which have no hookups (only Fishing Bridge RV Park in YNP has any hookups; otherwise you will have to camp outside the park), but there's a trick to that too - mostly arriving between 9 and 10 AM and just waiting until a site opens up. There's always someone who gets lucky, it seems, and advises folks not to bother with reservations, but I have seen people turned away because everything is booked solid. Don't risk it. You can use one base camp for both Yellowstone & the Tetons, though Mammoth would be the worst choice for this option (opposite side of YNP from the Tetons).