With the size of your party, you should be able to get a group rate at any hotel. Be sure to ask for Group Reservations when you call.
The Hotel Monteleone <http://www.hotelmonteleone.com> is one of my favorites in the French Quarter. I wouldn't consider it inexpensive but it's in a great location to visit all of New Orleans' most popular attractions and it's been recently renovated.
To save a few dollars, you might also check out both the Holiday Inn <http://www.holiday-inn.com> and Best Western <http://www.bestwestern.com> chains. Both have hotels right in the French Quarter that are probably a bit less expensive than the norm.
To really save money, you could avoid the French Quarter altogether and stay out in one of the 'burbs, but I wouldn't recommend that if you're on a short visit. New Orleans isn't known for its great public transportation system.
And by the way, if your visit falls during Mardi Gras week (the week before Ash Wednesday) all bets are off. Bargains will be hard to come by!