I might actually road trip to Cleveland for the game. Never been there before. Anywhere I should go/eat on Saturday night if I do make it?
Disregard Great Lakes for food (and their somewhat overrated beer). Check out Market Garden in Ohio City (it's about 2 minutes from downtown). They craft their own brews on site and their Festivus ale is one of my favorite beers of all-time. Granted, Great Lakes is a short walk from there, so you could still stop by for a beer or two. However, Market Garden would be better for food. If you wouldn't mind venturing out a little further, Melt Bar & Grilled is probably the best place you can stop for amazing food at a reasonable price. It also has a great selection of beers, but it typically has a long wait. (I'd suggest going to the Independence location and sitting at the bar area, which is first-come, first-serve.)
I guess it really depends on where you plan to stay and how far you plan to venture from there. In terms of a wide-range of food/drink options within walking distance of each other, checking out Ohio City would probably be the most fun. Ohio City Burrito is also good if you want a quick bite and just want to tour the bars around there as well.