Beignets at Cafe du Monde are pretty much mandatory. Beyond that, Stella, Stanley, Cochon, Luke and August are fantastic (though it's really, really easy to eat well in New Orleans). If you can venture a bit further, love Cake Cafe for breakfast, Creole Creamery for ice cream, and Dante's Kitchen for brunch.
I'd also really recommend getting out of the Quarter (not hard to do via taxi or streetcar) to the Garden District. Beautiful architecture, a little less touristy.
Sigh. Must plan a trip soon. Have fun!