I'm not opposed to "Devastation Tours" because I think they can be quite educational. I've given some myself. However, I've lost count of the number of people who tell me they "saw the Katrina destruction"... as they whizzed by at 70 mph on I-10 through New Orleans East.

However, to stay on topic for the OP, this is what my suggestion would be, given your time constraints:

In Baton Rouge, try to see Tiger Stadium, aka, "Death Valley" and Mike The Tiger's enclosure (yes, a live Bengal tiger) and maybe a walk around campus.

Drive to New Orleans on I-10 and get off on the Carrollton Ave. exit. Drive straight on S.Carrollton towards St. Charles Ave. You could stop at the Camellia Grill (626 S. Carrollton) for a late breakfast or early lunch. Make the left hand bend onto St. Charles Ave. and you are now in the Uptown area. You'll see the streetcars, Tulane and Loyola universities, Audubon Park and lots of mansions.

Turn right on Napoleon Ave. and then left at Magazine St.. You'll see some of the funkiness of the street along with more interesting architecture. As you get into the Lower Garden District, you will have to bear left onto Camp St. from Magazine St.. Follow Camp into the Warehouse District, you'll pass the D Day Museum (National WW II museum). Continue into the CBD and park between Poydras St. and Canal St.. At this point, you can walk to the foot of Canal St, see the Mississippi River, spend some time at Harrah's Casino and walk into the French Quarter. You should be able to park for free on the street since it is Sunday.

When finished, drive away from the river, either on Poydras or Canal St., towards S. Claiborne Ave.. Take a right on S. Claiborne and go straight. After you cross Canal St., it becomes N. Claiborne. You can follow this all the way to the Lower 9th Ward. After you cross the Industrial Canal bridge and you get to the bottom, take the first left turn and you are in the Lower 9th where Brad Pitt's foundation wants to build houses. If you would continue on N. Claiborne, you would eventually enter St. Bernard Parish (about another 5 or so minutes).

When you've seen enough, find your way to I-10 and head east to Biloxi. This should give a good mix of the New Orleans area and help you accomplish your goal.