A little farther but definitely in walking distance, the Corner Tavern on Mass Ave. Mellow, cozy, plenty of TVs, the food is way better than at the other places mentioned (in my opinion). I mean, it's not a sports bar per se, but I've only ever gone there to watch a Sox game.
421 Marlborough St, Boston, MA 02115
*sigh* I miss working in Copley Square. Someplace different to eat every day.
For Boylston street options:
If you want to watch the game, you've got the following choices:
McGreevey's is the only "real" sports bar in Copley Square, other than Champions, and their food is good (other than their burgers, for some reason).
The bar side of Uno's has many TV's, and you know what you're going to get with the food (stick with the pizza)
Pour House has great beer, lots of TV's, and . . . food.
Whiskey's has many TV's and pretty good food. Service can be meh.
For some reason I never went to Daisy Buchanans, but that's another option (ok, that's Newbury, but really close to Boylston)
A bit further away, on Dartmouth Street is Clery's, which just changed their menu (only been there once since it changed, looks like the Met Grill's burger bar menu). Lots of TVs and good beer there.
That should get you started
907 Boylston St Ste 21, Boston, MA 02115
240A Newbury St Ste 1, Boston, MA 02116
Clerys Bar & Restaurant
113 Dartmouth St, Boston, MA 02116