I don't mind a Baskin Robbins, and I hear those Marble Slab & Cold Stones are good, but I've never been.
There are a couple of phenomenal New Orleans ice cream joints I would highly recommend though.
#1 Angelo Brocato's on Carrolton. Been reopened for a while, and is a New Orleans tradition. If you don't want spumoni or torrincina, there're plenty of other flavors to choose from, including italian ices as well.
#2 Creole Creamery on Prytania. Rich delicious high-butterfat ice cream that makes ya mouth go wow. It's also kind of cool, because it's an old McKenzies and still maintains the same storefront.
#3 Gelato Pazzo Cafe. On Oak St. near Carrolton. It's a new place, and a little pricy, but you talk about delicious. Rich, fresh, flavors. The TLC they put in every batch is palpable on the tongue. I hear they also do paninis & stuff, but I've just been there for the gelato.