@JDawg
I'll start with stuff close to your hotel and the stadium.
Fin & Fino is a good option and close to the hotel.
There is a good oyster bar (Caroline's) and steakhouse (Dean's) in the new JW Mariott, which I assume is near where you're staying.
La Belle Helene is a good fancy French place, but not too fancy.
Mariposa and Bernadin's are also close by and are nice places.
Ink & Ivy is a decent option for drinks anytime. I'm sure someone will say it's an awful place, but the interior is fairly upscale, it's a big place, and you're going to be surrounded by people going to a football game most of the weekend. There is also a cluster of bars at French Quarter which will cater to football fans. Just google it and you'll find it, no problem.
Good rooftop bar at the top of the Kimpton called Merchant and Trade. Another good one is Aura at the JW Marriott, and the one at the top of the Grand Bohemian. Graham Street Pub and Patio has rooftop but is only a couple of stories and over by the stadium.
The night before the game you might want to take a short trip to SouthEnd. You can take the light rail a few stops, Uber, or walk. There are a lot of breweries, restaurants, and bars there and you won't be as trapped by the Pack/Terp crowd. A lot of that is also walking distance to the stadium, so it will fill up on Friday morning or after the game.
Let me know if you need more.