Dauphin Island (just south of Mobile) has some of the nicest beaches in the continental US.
If you get into LA, I'd suggest going to Lafayette for a few days. Partying in Cajun country is a thing to behold, lots of amazing back porch bars and amazing food (amazing food everywhere..)
- this along with spending as much time as you can in New Orleans. That city exists as an anomily in the USA.. it is its own separate entity and one of the most amazing cities I've ever seen to. There is such a unique clash of cultures there. Going to some of the blues/jazz shows around fisherman's district is a must.
I really enjoyed Savannah. That city has a really vibrant arts scene and is pretty progressive. The whole downtown core is really fun to rent bikes in and rip around.
I'd maybe just suggest driving at least the gulf coast and taking it all in. Some cool towns along the way to discover.