New Orleans is a very dangerous city that is fun for a night or two if you know where to go and love the bar / club scene or are into freaky deeky sex stuff. Also some excellent food.
Otherwise the city is a fucking third world pit with the exception of a few small areas. Which for tourists is mostly the french quarter.
If you go, hit:
Audubon Zoo
River Walk area
Take a ferry down the river
French Quarter / Bourbon St
Aquarium is not worth paying for.
Can easily be done in two days. Don't stray off the tourist areas or you will be mugged / raped / Killed.
Mardi Gras is best avoided. If you want a some what crazy night but not deal with millions of people all pissing, shitting, blowing, fucking, puking etc all over each other then go during Halloween or some other time. Mardi Gras, unless you are a total booze hound and into parades in some huge way, is best avoided.
The other places in your list are all > New Orleans.
The best way to see NO is to hit a cruise out of there, spend the night before and go out and see the 5 blocks worth of clubs and shitty stores it has to offer and hop on the ship for a river cruise out to the Caribbean.
Pick your strip clubs carefully unless you are frequent the SS forum and enjoy Fedor posts.