There isn't a bad spot in the Tetons. I actually hiked up to Paintbrush Canyon and camped there. Totally worth the hike. The park has bear canisters you can borrow.
The Suwannee River Camps are some of the best. They are only accessible by boat. Each site has campfire rings, screened in rooms and bathouses.
Some sites are close together, but still have trees between them. Weekends are busy, but the weekdays are fantastic. You can rent kayaks on site or bring your own and explore the Intracoastal.