My wife and I traveled with her mom and sister. We stayed two nights at the Hyatt French Quarter. It's a really nice hotel with a great location. Be sure to go to Emeril's (Emeril LaGasse's restaurant) the food is amazing. We enjoyed our stay in NOLA doing things like going to Cafe Du Monde for Beignets and walking down Bourbon St. at night.
Boarding the Carnival Conquest was a breeze if you get there early (around 11:00 am). The whole embarkation process took about 30 minutes. However, if you wait until later (like my wife's mom and sister did), it can take 2 hours to go through the embarkation process. The conquest is an absolutely beautiful ship, especially if you enjoy impressionist art. My wife and I have been on 13 cruises, and we both though this was the most beautiful (and I'm not even a fan of impressionism). The ship was also kept impeccably clean all the time.
Our cabin was tastefully decorated, comfortable and spacious by cruise ship standards (Carnival tends to have the biggest staterooms of the moderately prised cruise lines).
Room was tastefully decorated, very roomy by cruise-ship standards, and comfortable.