There are several plantations between NOLA and Baton Rouge you can tour, and having a car makes visiting them a lot easier. I've been to Laura, Oak Alley, and Nottaway (saw them via tours out of NOLA) and they're all excellent. Also consider Destrehan, San Francisco, Madewood, and Houmas House. You'll probably want two days to see them all, as house fatigue may well set in after touring four in a day.
You could also visit Baton Rouge -- the city itself is a bit on the grubby side, but has about a day's worth of attractions. Magnolia Mound is a plantation house in the city, similar to Laura in some ways. The current state capitol building is one of the country's best, and there's a state history museum nearby, the Capitol Park Museum. The Old State Capitol building, which looks a lot like a castle and home to a political history museum, is worth a brief visit as well.
Jackson, MS (also a bit of a grubby city) is on the way between NOLA and Memphis and has about a day's worth of things to see, including the current capitol building (very good), the old capitol (home to a state history museum), a modest art museum, the governor's mansion, and a civil rights museum in the downtown area, plus a few smaller historic houses to the north.