Grand Tetons experience anyone?

For staying inside the park, Colter Bay and Gros Ventre are your choices.
Colter Bay has two types: park campground or concession run campground. you can make a reservation at the concession run campground and it has hookups. the park campground has a dump station and water and flush toilets.
I personally do not like Colter Bay because it is in a forest without views of the lake or anything but trees and campers. But that's just me. :)
Gros Ventre is bigger and well shaded but has more open with views of the mountains. It has water and dump station and toilets and is close to Jackson which we like. There are many sites you can fit into.
On both places, try to arrive on Tuesday, Weds, or Thursday, in mid morning to early afternoon.
Generally, you will not need a/c. You are allowed to run your genny from 8a.m. to 8p.m. and they hold you to that pretty tight.

We have done first come at both Colter Bay Camp Ground and Gros Ventre Campground in June without any problems. I like Gros Ventre Campground the best.
If this is your first trip to the Tetons, I would advise at least a week.

My family and I camped at Gros Ventre campground. Awesome views of the Teton range and an occasional elk. We would go back in a heartbeat. Btw we were there in July. Easy access.

We stayed at Colter Bay Campground in mid Sep 2011 after working at Yellowstone. We did walk-in but had checked to see if they were busy then. The loop we were on was one way with sites on both sides of the road - we have a 37' travel trailer and chose one with the right orientation and size for our 3 slides.

It was easy to bike ride around to the sites.