I spent 14 summers going to GSP while growing up. We would spend 1-2 weeks there at a time and sometimes we even went 2 times per summer. I love that place! That being said, if I was going back with friends now, I would stay outside the park where there are a few less regulations. Maybe try to rent a house on the river where you can play dominoes all night, drink beer, and be as loud as you want. GSP is pretty strict about everything I just mentioned especially after dark.
For most years, we stay in campsites, 82, 84, 86, and 92. We had alot of people and took up that whole corner. That was also close to the river and we had that whole open field next to us to throw the football, baseball or whatever. We have also stayed in 102, 100, 98, and 96. Plenty of shade in all those campsites.