I've been going to Battery Park for at least 7 games. It's in the upper financial district where it starts to turn in to the Faneuil Hall area. For perspective, if Faneuil was in New Hampshire and State St was the border, the bar would be in Lowell. Just off Milk St, 3-4 blocks from State St, so very easy to get to. It gets fairly busy around typical weeknight game time, as many people who work in the area drink after work until 8-8:30. Definitely not "fratty" like many other places that have lots of tvs (looking at you, TITS). One of the bartenders now knows me and is very cool. They have a lot of tvs but don't attract the kind of people you'd find in Garden/North Station bars who really watch the games that are on, so they are always willing to put the game on at least one tv, even if it's against Stanford, even if it's on ESPNU, even if the Bruins/Celtics are also playing. Very decent prices for a city bar, and a decent selection too, as far as beer goes.
I'd say it's the best option for Boston proper. I've been outright denied at several bars. You don't want Garden/NStation area because they only want to watch pro sports, Beacon Hill and Back Bay bars have no tvs and tend to be expensive, Faneuil bars are overpriced and crowded, Seaport and South and North Ends are kind of out of the way and expensive, Fenway necessitates the use of Green (bleh), Chinatown duh, and none of the other Financial District bars I've tried match up. I have to say I have next to no experience with the BU campus or Southie though, so if someone here has found a good one there, please speak up.
Should we get a head count of who lives where so we could figure the most fair option for all of us?