I did a "staycation" honeymoon last year and went to a monday night saints game. We stayed here http://therooseveltneworleans.com/
It's walking distance to the Arena/Dome and the French Quarter.
There is a restaurant in the bottom floor called "Domenica" which is DELICIOUS and a pretty famous bar called "The Sazerac" where the sazerac (famous drink) was invented.
Dunno how much you are looking to spend but it is by far one of the nicest places i've ever stayed.
(also if you inform them when booking the room that its your honeymoon you'll get some nice surprises)