Buffalo is a GREAT city! I lived there from late 2006 - early 2014, so my info is a little dated, but I’m happy to make recommendations if you have any questions
Fantastic! We'll be going up Friday. We had thought about going to Toronto after the game on Saturday but am now reconsidering and thinking about staying in the Buffalo/Niagara Falls area. We'll likely pay at least one visit to the Seneca Casino to lose a few $$$. Any other reasonably priced restaurants/bars you might recommend? Other venues of entertainment? Thanks!
Okay, so all of my experience is a couple years out of date, so I'd recommend getting second opinions, googling, etc.
Wings: Anchor bar is the first, and is a nice bar. Its near down town. Personally, I prefer Duff's wings, and there is one about 2 miles from UB stadium. It might be busy, and if you're eating there its no frills, but I like them. In truth, you'd be hard pressed to find a place that does a bad job with wings in Buffalo.
Other restaurants worth a look: Pearl Street Brewery. Probably my favorite place in Buffalo, this brewpub predates the big explosion in craft breweries by a couple years. They've got a BIG restaurant/bar (several bars) Downtown. Great food, usually have a dozen or more great beers on tap. This place has several bars (indoors and outdoors) spread across several floors depending on how busy it is and the weather.
Honorable mention: Ulrich's Tavern. This is a German themed bar/restaurant that dates back to the 1860 (and once appeared on No Reservations). Its under new management since I lived there, but I was there a few months ago and it still felt like the same old place.
There are a ton of other great restaurants around Buffalo, but those are my top recommendations.
Bars/bar areas: So far as bars districts go, you've got 3 options, none of them particularly near UB's North Campus (where the stadium is located):
(1) Elmwood Village area - This is a Court Street like area near Buffalo State Univeristy (in town, probably 20-30 minutes from UB North), good mix of nice and college/20-something type bars and restaurants (if you're in this area, I'd definitely recommend checking out Mr. Goodbar and Coles, among others). This was the area I went out in the most.
(2) Allentown - Another bar district, nothing too fancy here. Lots of divey bars (who knows, maybe some super nice places now), usually a fun time. I can't think of any places I'd recommend or disavow off the top of my head.
(3) Chippewa Avenue - This is basically the downtown, much clubbier bar scene. I rarely if ever bothered with this area (not my scene), but its an option for some (strikes me as more the area Miami folks might go, not so much a place for right thinking, bar loving, OHIO grads :) )
Those are just the 3 heaviest bar areas that come to mind. There are hundreds of neighborhood/local bars, nice bars, strip-mall bars, trash bars, bars where you might die, etc. Since I've been gone, there have also been a huge number of craft breweries open, but I can't really speak to them (I'm sure they're fine).
Drunk food: Depending on how your evening (and our game) goes, and just how unhealthy you want your weekend to be, Jim's Steakout serves up large, fatty, delicious sandwiches. NOT RECOMMENDED FOR ANYONE WITH A HEART CONDITION (and probably not a good idea for anyone else)
I'm not really a casino guy, so I can't speak to that. Niagara Falls is fun (remember your passport if you go: the views from the US side and Niagara Falls Park are AMAZING, but the city of Niagara Falls NY isn't any place to get excited about). Other than the Seneca Casino, Most of the touristy bar/restaurant stuff is on the Canadian side. Canadian ballet is also an option, if that's your thing, but I've never been to any of those establishments in that part of Ontario.
Hope this helps, happy to answer any other questions! Enjoy your trip!