I am planning a hang for July 15-17 at Fall Creek Falls State Park in Tennessee. Here is the .gov site http://www.tn.gov/environment/parks/FallCreekFalls/
The camping section says there are "3 primitive camping areas on the overnight trails" so i'm thinking one of those would be good. I called to make sure hammocks were accepted and got transferred to an ever ringing phone. I'll try again later.
If there is enough interested people who want to join me i'll start a sign up sheet.
-edit. I got a hold of someone on the phone. They didn't know of any rules against hammocks. We'd need to stop in and get a permit to back country camp but the permit is free. There are designated camp sites off both overnight trails. This means its a go for me provided the interview i'm waiting to line up next month doesn't just happen to fall on that Friday, but even then i'll head later in the day.