After giving this a little more thought for golf guy, I'd suggest for future posts about destinations, that you give some more specific info. Such as, the exact days you'll be in a particular location, the specific hotel, etc. It would help us to give you better suggestions. Also, when you ask for "reasonably inexpensive" places, what's inexpensive for me might not be for you.
With that said, a few suggestions. I'm assuming that y'all are 20 something's on a budget.
If you really want inexpensive, you could try Rouse's supermarket in the Warehouse District (701 Baronne). It's local, very large with everything you could possibly want, has a wide variety of local hot & cold prepared meals to eat in or take out, tables are near the cash registers and is open from 6 AM til midnight. They also have a branch in the French Quarter (701 Royal) which is much smaller, open from 6 AM til 1AM.
http://shop.rouses.com/storelocator....lyads.aspx?r=1
A couple of inexpensive restaurants in the CBD (central business district):
http://www.therubyslippercafe.net
(You want the one at 200 Magazine St. Breakfast & Lunch only.)
http://www.redgravycafe.com
(Open for breakfast, lunch & dinner)
In the FQ, you can try:
http://johnnyspoboys.com
Don't know if any are open on Mardi Gras. Check the websites for exact times or call them.
There will be lots of restaurants open in the Warehouse District, CBD, & French Quarter, but I don't know how many will fit your budget or that you'll be able to get into because of the crowds.
Good luck and have fun.