Oh, there's a restaurant, um, pretty famous, shoot, I can't think of the name. Starts with an M? Is on a lake with a pier out back? Middendorf's. Not actually very far from New Orleans, but worth a bit of a detour and a stop if the timing works out for a meal.
Avery Island used to be a fun visit. Tabasco and whatnot. I want to say some kind of bird refuge is there, as well as the hot sauce plant and salt domes - you might have to call ahead for tours.
Haven't been to Sea Rim, but I think I heard good things about Kemper Williams State Park, but I don't recall specifics. I don't know that I can dig up my reference books in time to help you out, but maybe I will try. I need to look for something else in the shed this weekend, anyway, if I don't melt.
Things to see in Baton Rouge - the Old State Capital is nifty and the new State Capital has some nice features. If you happen to be in the area and want to stretch your legs and look at architecture. Probably there's more stuff since I left, but I can't think of anything worth going out of your way for. Unless you want to make a pilgrimage to the bar that Laura San Giacomo worked at in sex lies and videotape, I suppose. Kind of a bitch to park near there, though. Coffee Call for beignets and coffee if you don't want to wait to get to NO for that. I'm sure you can get beignets and coffee in Lafayette, come to think of it, but I don't know where to recommend out there.
Oh, if it's too hot for you in NO, the aquarium is air-conditioned and worth checking out if you like that sort of thing. It makes a nice touristy break if you are out and about in the Quarter of an afternoon and get hot but don't want to call it a day. The Mint is right there at the edge of the Marigny, too, though I've only been there when they had special exhibitions, I don't know what it's normally got going on (although I did enjoy the exhibits that were about making coins, which they presumably always have). And you have a car, so the Degas House and Museum of Art (I love the sculpture garden, but it is outside and so of limited use i escaping the heat) are options.
Heh, in honor of the beginning of football season the keepers of the dress code at work declared today NFL Jersey/T-shirt day (normally stuff with logos is discouraged) so I wore my Deuce McCallister jersey that a lot of people from outside my department recognized enough to come talk to me and ask if I was from New Orleans, etc., so I am all nostalgic. Hope it may be of some benefit to you, Lee!