For those of you badmouthing my beloved Cleveland (I'm originally from West Seneca), stop it. You don't know what you're missing, and you can only wish that Buffalo was as great a place to live as Cleveland. I've lived in both cities in the last 10 years, and Cleveland is light years ahead of Buffalo in all aspects of life.
As for places to eat after the game, go to Panini's in the Flats. Get an overstuffed turkey sandwich and a beer or two. The sandwich is grilled turkey, cheese, fries, and coleslaw on freshly baked bread. Very satisfying after a night of whooping it up.
East 6th street at the top of the Flats has a lot of happening joints.
Jacobs Field is not the mistake by the lake. It is one of the nicest ball parks in the country, smart guy.
Big Tribe bars are anything open on E. 9th Street before the game.
Bars close at 0200, which is difficult for Buffalonians to comprehend (it was tough on my brother and his buddies when they came for weekends - they couldn't get used to going out at 9PM instead of 11PM!).
Have fun! Cleveland is a great place!
PM me for more information if you'd like.