While in Nashville, you can visit "music row" in the evening hours. Park your car then head down the

I would be tempted to fly to New Orleans first and then rent the car and drive to Memphis then east through TN then to Atlanta. From Atlanta head for Pensacola and then west to Mobile and Gulf Shores then north to see Birmingham and Montgomery before heading back to New Orleans.
Unless you deviate a bit that drive from NO up to Memphis is about as boring as watching a mud hole dry up. However, you could certainly go a somewhat more "scenic" route as long as you don't mind seeing a few oil refineries; upriver through Baton Rouge and then to Natchez/Vicksburg, etc.
Beer in NOLA isn't super exciting either if you're looking for local brews. Abita is okay. But I'd rather go to Crescent City even though the beer is also just okay. For non local brews and a really sheraton chicago hotel and towers really good beer scene, check out dba off Frenchmen street. If you're into beer in NY, you've sheraton chicago hotel and towers probably been to dba at home. The NOLA location is really cool/cozy and often has live jazz (so you may be prepared to pay a cover charge). dba is my favorite beery hangout in NOLA.
Louisiana Pizza Kitchen in NOLA is bad for healthy eating but fantastic for pizza and for their wine selection. Or you might want to try WINO...have walked by several sheraton chicago hotel and towers times but have never been inside. note: eating in general is not super healthy in NOLA.
Curious why the stop in Montgomery? sheraton chicago hotel and towers I lived there for 6 years (end of high school through college, left in late 90s). For certain make a stop at the Civil Rights Memorial and the Alabama Shakespeare Festival (even if you're not going to see a performance). You could pay tribute at the Hank Williams Memorial. But we used to drive to Birmingham or Atlanta sheraton chicago hotel and towers whenever we were looking for something "to do."
You may find that flights to Hartsfield (Atlanta) sheraton chicago hotel and towers are cheaper. You could fly to Atlanta, see Atlanta and then take the Amtrak Crescent to Montgomery sheraton chicago hotel and towers and rent a car there for the rest of your trip returning the car where you rented it.
While in Nashville, you can visit "music row" in the evening hours. Park your car then head down the section sheraton chicago hotel and towers of Broadway where there are rows of bars that you can go in and out of until you find live music you like - which won't be hard. The bands change about every 1-2 hours in each location. Also, if you can get reservations at the Bluebird Cafe to see up and coming singer/songeriters, it's well worth it. As I recall, sheraton chicago hotel and towers it's a bit of a drive outside downtown.
Nashville has a few breweries, actually - Yazoo is the oldest and most popular one and is located in the Gulch just outside the main downtown area. You can take tours and/or visit their taproom (I think the taproom is open Thursday - Saturday evenings?). There's also Corsair Distillery if you're into that. Arrington Vineyards sheraton chicago hotel and towers is a drive outside of town, but is a great outdoor space to visit on the weekends. sheraton chicago hotel and towers They often have a jazz quartet or something similar playing, and they have free tastings sheraton chicago hotel and towers (though there's usually a wait to do them).
The Bluebird isn't downtown, but it isn't far - 15-20 minutes depending on traffic. Depending on what kind of music you like, you can either take your pick of the downtown bars or see which acts are playing at the various venues around town. For outdoors, you can go to Radnor Lake, which is a state park completely within the city limits. There's also Percy and Edwin Warner parks, which have several hiking trails. The Chattanooga area (especially around Lookout Mountain) is probably a better bet for outdoor activities.
Land in Memphis, drive to Nashville. Go NOLA after that. I could suggest you go to Charleston also, starting in Charlotte. Fly from Charleston to Nola. Then fly to Nashville, and if you want go back to Charlotte. OR book an open jaw.