Sports Academy (
http://www.sportsacademy.fi/)would be your best bet, then places like Sport Chelsea Pub (
http://www.chelsea.fi/) and Aussie Bar (
http://aussiebar.net/) are possibilities.
But, i doubt it, as those games usually start at 7pm ET which is 2am in Finland, just as those bars as closing (Sports Acad 3am). Im sure there will be a couple of 'local' bars around the centre that could show it too, but the time will again be the problem - i dont see many still being open at 5am when the games finish!
What hotel are u staying in, maybes they have Viasat hockey channel?
Im sure the hockey on the ice will be good enough for you? are you waiting for individual tickets sales or have u been ripped by a package deal?