The back (inside w/AC) bar at The Lime Inn usually has sports on. And, they are pretty good about letting you watch what you want. Couple that with the mussels and it's all good.
I vote for the Quiet Mon, I think it's an essential island experience, you gotta go there to meet Kenny (the bartender, not THAT Kenny) if nothing else, he's a great guy. It's fun watching the game there on a Sunday afternoon and I'm not even a football fan.