There are some very good recommendations above, so if I am repetitive, it is only to drive home a point
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First, while it sounds touristy, the suggestion to do a Duck Boat tour (about $30/person I think) is a good one, if weather complies. You see a lot of Boston, and from some interesting vantage points.
Second, there are a bunch of bars that cater to different tastes near the TD Banknorth Garden, so you can check those out on game night. Boston Beerworks is good if you like microbrew, Sullivans tap is good if you like cheap booze, McGann’s is good if you like politics (there are pictures of John Kerry and William Weld drinking pints after running against each other in the 1996 Senate elections).
Third, given that you are there on St. Patty’s day, take seriously the suggestions to go to Southie or to Doyle’s in Jamaica Plain. The problem is that they are located far from each other, so you may need to decide between the two. If you are a movie buff, opt for Doyle’s per Brick’s comments above, but Doyle’s is also a place to go if you like politics (eg: early pics of Mayor Menino on the wall, plus lots of other stuff – my wife used to work for the City of Boston, and the union had events at Doyles – I love the place).
Four, if you want a good view of the city, go to the restaurants at either the Bay Tower (60 state street – near fanueil hall) or Top of the Hub, atop Prudential Center. Now, the trick is that you just go up to the bar, and then have a drink while taking in the view (and I think there is also a separate bar menu at both places).
Five, have fun!