The Sugar Bowl is the night of the 1st and I don't think you'll really have a problem with the crowds after that. The big crowds would be in the days leading up to it. The morning after we won the National Championship in 04, the city was literally a ghost town. It might have still been too early (and people too hungover) but the interstate heading back to Baton Rouge was PACKED. I think y'all will be fine in the city though.
If I were you, this is what I would do (not really sure if this is BEST solution and how well it would work, but it's what I would do to bypass the crowds). I'm assuming you're flying into MSY in New Orleans (well I think it's Kenner). I would schedule my flight to land right around kickoff and travel to your hotel during the actual game. I would say the majority of the people will either be in the Superdome at this time or in bars watching the game. If you're staying in the Quarter you can completely bypass the area around the Dome (Poydras St., Canal). Do you plan on renting a car or taking a cab? Keep in mind that the streets in the Quarter are usually one way and only one lane. Traffic can get backed up. Avoid crossing Bourbon, in a car, at all costs! There's so many people it's pretty much impossible to get a car across that street. If you have to cross Bourbon, I'd do it as far away from Canal as possible.
I don't mean to scare you with all that, I just hate driving in that city. I really don't think you'll have any problems, I just wanted you to know what was going on and how to avoid it the best you could. I think you'll enjoy yourself so much more if you have a plan set up. You know how people talk about having an awful time in Disney and they failed to plan? I really don't want you to be disappointed with NOLA! I think once y'all park though you could walk around the Quarter that night. The crowds may not even be that bad. I'll let you know a little better what to expect once the teams are announced in the beginning of Dec. But, the fact that the National Championship isn't in NOLA this year, works in your favor.
After the game the majority of the people will head to Bourbon (which is in the Quarter). The crowds may not be that big since a National Championship isn't involved (the National Championship is also in NOLA every 4 years). Here's pics from the last one LSU won in 2008 (we've won the National Title the last 2 times the game has been in New Orleans - not to brag or anything
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This is of our head coach holding the trophy on a balcony on Bourbon...
...and this is the crowd below!
Yes, they are on the actual street!
But honestly, LSU is the team that will travel the most (IF we're in this game) and even if we win the Sugar Bowl the Quarter will not be nearly that bad. I'd say the partying would go late into the night but not into the early morning. Also, as long as your hotel isn't on Bourbon, you probably won't hear much of it. I'd snap as many pictures as you could of the craziness, people may not believe you! Haha!
Ok some other things that aren't football related
Cafe du Monde - Yes! Do it! Find a table yourself, sit down and they'll come serve you. Bring cash!! One of my favorite photo opportunities there is to put the powdered sugar on your nose and take a family photo! Haha, it's so cute! I always get the frozen cafe au lait and it's AMAZING!
The French Market - It's down St. Peter's from Cafe du Monde. There's so much neat stuff to look at. It's like an outdoor flea market.
Mother's Restaurant - Looks like a whole in the wall, but the food is SO good! Sometimes there will be a line out the door, but it moves pretty quickly. It's on the corner of Poydras and Tchoupitoulas. Pronounced: Chop-a-TOO-lis.
Audubon Zoo (Garden District Area) and Aquariam of Americas (Near the RiverWalk) - These are great! If you had to do one of the two though, I'd go with the Audubon Zoo if it's not too cold.
And just explore the Quarter. It's so full of history, I love it! Me and my BF took a ghost tour back in November and it's not scary at all. It's just like a history tour. I suggest doing some sort of walking tour in the Quarter. I always wanted to do one, but it seemed kind of touristy. I loved it and can't wait to do another one.
It really is a great city and I think y'all will have alot of fun. And seriously, if you have any other questions, I'd love to answer them!