Just my two cents.....coming from barbecue capital (Kansas City btw I ship Jack Stack BBQ to NYC a lot!) we liked Dreamland (went to the Northport one) over Full Moon, hand Moes last time I was in town and it was ok.
I would suggest you go to Rama Jamas for breakfast before the game. The walls are covered with Tide memorabilia..it's no frills but deliciously southern (have the grits) in the nature of the food and the people who are eating there. It will be packed so get there early. It's on the corner of Bear Bryant across form the stadium..we have taken so many guests with us and they all comment on what a great experience it is. The owner is a Saban replica, a really nice man and will chat you up if he gets the get a sec.
I would also suggest that after the game (since it's early) that you walk to the strip. The atmosphere is electric after a win. Restaurants will be crowded but just enjoy the experience while you wait. Buffalo Phils will be packed but it's fun to go and there will be LOTS of students there. We found it so helpful to just immerse DD in the college experience.
I also think that Mugshots is another "not to be missed". The hamburgers are great and again..lots of college students. Magic Mushroom has great pizza (ok not NYC style but good)..again lots of kids
So my point is to take your DS where he will be with students so he gets the feel of the student side of campus.
One more thing..not sure if your DS is considering joining a fraternity but if he is y'all might want to call the Office of Greek Affairs and inquire to see if he could have a Greek tour. they have been known to hook you up with a couple of fraternity guys to go an visit some houses ect. As it has been discussed here making a connection early is important especially when it come to Fraternity Rush and being OOS. Their number is Phone: 205.348.2693. Hope you have a great trip!!! Safe travels. We will actually be flipping locations as I am on my way to NYC for Thanksgiving!