If you want to get away from people the last place you want to go is GC in the summer. There will be over 5 million visitors there, most of them this summer. I have been there several times and it is crowded. That is not even considering the parking/shuttle issues. Have also taken the train from Williams and I will say it is fun, but Williams will be crowded since it is a gateway for many GC visitors. Same with Flagstaff. While I understand your quest to see GC I truly believe that coming from Chicago will take more like 10 days minimum and be much more pleasant doing a 2 week trip.
RichH