Well, I don't know so much about the eating part... but the Daiquiri spots certainly hold a special place in my heart during the parades & I like the vendors that set up their food stands along the routes - just more Carnival atmosphere!
For the uptown parades, Sophie B Wright on Napoleon Ave. Their fried chicken is outstanding, but their catfish is absurdly good. They also have bathroom passes (kids are free) and it's for a good cause.