Baton Rouge was settled by the Spanish, then the French and also the Germans. The English came last. Spanish Town is an interesting, funky neighborhood for just walking through, if you like that kind of thing.
The Rural Life Museum is not your traditional museum. It is one of the few outdoor museums in the country. The focus is on rural life in the 1830s -- life off the plantations. Most of the buildings are authentic and were moved there in the 1960s and 1970s. Windrush Gardens are also on the grounds and the azaleas should be in bloom.
The Old State Capitol -- we call it "Hogwarts on the Mississippi" -- and New State Capitol, which is an Art Deco gem are downtown and walking distance from each other. Also in that area is the Louisiana State Museum. It is not a "typical" museum -- well, the first floor is more or less, although it does have a real shrimp boat, but the third floor is definitely different. It provides exhibits on each region of Louisiana and includes a dozen or so listening stations which present the history of the music of Louisiana. If you're into music, you definitely want to spend time there. There's also an exhibit on Mardi Gras.
LSU campus is worth a look, if you want to get out and walk around. Mike the Tiger has a million-dollar habitat; he's one of only two live animal mascots in the U.S.
Magnolia Mound plantation is not bad, but you'll see plenty of plantation homes on the drive down to New Orleans. It might be worth going to it because it is more typical of the average home than the ones on the River Road.
Oh, and if you're going to Little Rock, head over to Hot Springs. It's really fantastic.
Edited: 1:28 pm, March 06, 2013