Just visited Boston 2 weeks ago and went to The Harp Great Bills atmosphere! Got there 90 minutes early for the Balt game and found a seat easily - probably could have gotten a seat 1 hour before, but about 30 minutes before Kickoff, every table was taken - all Bills Mafia! Food was fine, service was good.
If you are alone, I think you could find an occupied table and ask to sit with them - that happened to me, a nice elderly lady was alone and asked to sit.
For KC, not sure how early, but I suspect you want to get there early.
Good luck and GO BILLS!