Get to Hammer's Lot EARLY! It fills up quickly.
I've only been to Buffalo a couple of times so I only know so much of what to do.
Definitely check out Niagara Falls, it's great. I second what @Inigo Montoya says by going to Wegman's. It's a great grocery store and perfect for stocking up on whatever you need.
Charlie The Butcher's is another nice place for Beef on Weck, but I have not been to Bar Bill, and I hear they are excellent
Dinosaur BBQ is another good place to try.
As far as wings goes, I agree that Duff's is a great place for just getting wings, but their pizza is nice too.
Paula's Donuts is nice if you want good donuts.
That's about all I've got. Have a great time, and thank you for your service. Once you've been to Buffalo for a game, you'll want to be back all the time. GO BILLS!!!