So there's a million recommendations out there already, but don't discount a new entry..
Archie Manning just opened a restaurant this year, called Manning's. Good New Orleans/Southern style cuisine and a big sports theme with tons of flat screens and memorabilia from Archie, Peyton, and Eli's careers. Cool place, and when I was there in February, Archie was even in the house on a random Thursday night, so I'm pretty sure he'll be there the week of the Final Four. Very personable guy.
And the restaurant is right across the street from the big Harrah's casino in NO... so there's that advantage too.
And everyone is right.. gotta have a Hurricane. O'brian's is a good place to get your first as you make your way along Bourbon St.