I would recommend using Urbanspoon.com when looking for places to eat. I found an amazing Thai place in Kingman, Arizona of all places. If you just put in the area you're in and check for good reviews, you should be able to find some really decent restaurants. Remember, sometimes the best places in town don't even have signs out front.
I would stay away from chains as much as possible. I mean, what a boring thing to do on a trip to a foreign country, you know? Not to mention the quality usually sucks. I'd definitely recommend trying out all the dinky little local places. Even if they're terrible, at least it will be a good story to tell later. I've never heard a good story that started "So, we went to Cracker Barrel, and..." Also, last I heard, Cracker Barrel was a super super racist company. Personally, I don't support that.
Anyway, since you'll be in the south, there will be a ton of local BBQ places to choose from. Go for dry rubs over sauces if you are worried about sugar content, and enjoy!