I've lived in Chattanooga my whole life (save a brief stint in Nashville this past year), but I have NO clue where to have my ceremony. I don't want it in a church, and I want to stay in the Chattanooga area. Reception-wise, I have a few ideas, but any others would be extremely helpful.
Depending on the size of your wedding, the Heritage House at Heritage Park on Jenkins Road in East Brainerd is beautiful. We had my daughters reception there. We discussed having the wedding there, but her finance wanted to get married in a church. http://www.chattanooga.gov/EAC/2919_eacHeritageHouse.htm
The Hunter Museum is a lovely place to hold your ceremony and reception! Perfect for an evening wedding/reception, and the views are gorgeous! There is info on their website about renting the facility if you are interested: http://www.huntermuseum.org/about/rent-our-facility/