DW & I just made a 8000 mile loop from SE Texas this past Sept 1st, our first major stop at Mt Rushmore & Crazy Horse. We stopped at Y-stone next, stopped next at crater lake oregon (unbelievable natural beauty)then went into NW Calif to see the redwoods, then down to Yosemite.
We saved Tetons (& more of Y-stone)along with Glacier for next trip! We were hesitant about going out of the way to Rushmore, but very glad we did. We enjoyed crazy horse just as much. I know for us, it was time to take a more than brief stop when we reached Mt Rushmore.
We left Sept 1st, was gone 6 full weeks. We had no issues getting spots, we would just call ahead early in the day to check availability. Very nice weather with lot less people going in Sept! The "grand canyon of Y-stone" & "bear tooth pass" is 2 places you must see. We stayed the whole time at Y-stone at "Yellowstone's Edge RV". It is a 30 mi drive to the north entrance, but my what a beautiful place to park your RV with superior camp hosts!