Hi, we were just there, went through Headwaters just to check it out in mid September and looks like a really nice Campground, has a large lodge/restaurant, and lots of security, but I thought it was terribly overpriced! However the Campground did appear full.
We actually had planned to Boondock off of Grassy Lake Road- access is right there at the headwaters...
Instead, we took YS Rangers advice and drove through the Tetons and over to Mormon row-- where we Boondocked on National Forest land :-) loved the FREE Price Tag. Also it felt like we were truly camping vs in a CG. (though we still had about 5 neighbors, just completely different feel to it...) Oh! And there were fire rings
Colter Bay was a really nice area, and it didn't seem much different than the parks we stayed at up in Yellowstone. If I had to choose between the Headwaters & Colter Bay, I probably would choose Colter Bay bc it seems more Central to all things in GTNP..
But if I was feeling really adventurous, I would be camping right out there in the National Forest :-)
There was an amazing view of the Grand Tetons from our TT, and it did rain, but it also snowed a little bit, it was just a wonderful time :-)
I'm sure wherever you decide to stay, you're going to have a great time too, this National Park is just incredibly beautiful