i'm from outside of NOLA, but I lived in BR for a while. You have to skate the Centroplex...best spot of all time. Its right in the middle of downtown. Smooth brick tiles, ledges for miles (though some of em are pretty shitted up due to BMXers), and just about any size stairs you could ever want to skate. Follow the footbridge across to the river, and there are even more spots (more stairs, some ledges with angle-iron over a sand gap). The tranny walls pictured above are also a must, just stay away from the windows because they will boot you in a minute. You should check out the catfish banks too. Its a parking lot with a bunch of concrete humps that make really fun hips; they're right under the interstate near the river. Other than that, there are lots of random spots dotted around the suburbs, but you might need to ask some locals for some specifics. I'm sure you'll run into someone at any of the above listed spots.
For food, you should check out Raising Cane's chicken fingers (a local favorite), Louies (for diner type grub), and the Chimes for something a little classier. These are all found at the North gate of LSU campus. For nightlife, check out The Spanish Moon for shows, and any of the bars on Chimes street are cool (at least they were when I lived there), just watch out for white thugsters and gutterpunks. Kids used to get seriously beat down out there on the regular. Also check out Red Star downtown for an artsier vibe. DEFINITELY avoid the frat bars, most of em are in an area called Tiger Alley; trust me, just stay away.
BR is pretty chill and laid back; you'll have fun.