If you are a backpacker it will be hard to find a better backpacking experience than the Teton Crest Trail. The views are amazing, the trail is in great condition amd your chances of seeing wildlife are very good. The entire trail is about 40 miles long, if you start at highway 22. We did the Crest Trail the last week of July 2009. Instead of doing the whole trail we took the tram up from Teton Village and backpacked from there to the String Lake Trail head. When we went water was plentiful and we carried to liters at the most. Mosquitoes were annoying, but not terrible.
The National Park requires bear canisters for storing food along the trail now, and you can borrow them at no charge at the ranger stations. If you are staying at the group sites they have metal food storage boxes you can use instead of the canisters.
Our favorite campsite was Death Canyon Shelf. The campsite is on a shelf with high cliffs immediatly to the West and a thousand foot drop and the Teton peaks just to the East. Water was flowing right behind the group site we were in.
As far as the car camping campgrounds, we stayed at Colter bay one night and Gros Ventre (pronounced Grow Vant) two nights. The Colter Bay site was small, closed in and very boring. The Gros Ventre campground was much nicer, in a wooded area with sites well spaced. Jenny Lake campground is by far the best campground (tent only), but it fills very early, some times by 8 or 9 a.m. If you need a shower, they are available at Colter Bay and at the rec center in Jackson (closest to Gros Ventre).From the NPS
Located in northwestern Wyoming, Grand Teton National Park protects stunning mountain scenery and a diverse array of wildlife. The central feature of the park is the Teton Range - an active, fault-block, 40-mile-long mountain front. The range includes eight peaks over 12,000 feet (3,658 m), including the Grand Teton at 13,770 feet (4,198 m). Seven morainal lakes run along the base of the range, and more than 100 alpine lakes can be found in the backcountry.
Have you visited Grand Teton National Park?