I would avoid New Orleans, it is overrated and nothing really special IMHO. Bourbon street is a good time if you like night life, drinking, and or live music. Other than that it is a dump and it really isn't that safe of a place. Cajun food is something special though.
The Trace is wonderful if you want an easy-going two lane road with no commercial traffic. I like going on it for an hour or two, but I get tired of the 50mph speed limit. They are not afraid to give tickets for going 5 mph over the limit.
I would recommend you make it over to Robbinsville, NC. It is probably 2.5 - 3 hours from Nashville. That is some of the best riding east of the Mississippi River.
V Strom 650, KLR 650