I went to New Orleans for the Sugar Bowl this January, but I am in no way a NOLA know-it-all. I just wanted to tell you to check out the Fairmont. That's where we stayed and it was very economical, yet close to everything to which you would ever want to go. It's an older hotel, so you get some of the history, along with the decent prices.
If I was going to NOLA again, I would try the Fairmont. We had a great time and even got to bring our little dog.