If you're looking for a crazy, uninhibited, DRUNKEN good time, then Faneuil Hall is the place for you! It's like all of the college keg parties you've ever been to, all rolled into one. Believe me, you definitely won't run out of places to see before curfew hits at 2am! You have a wide selection of Irish pub-type places, like The Black Rose, The Purple Shamrock, Kitty O'Shea's, etc, as well as places that have more of a "club" feel, like Parris and Q. Whatever it is you're looking for, I'm pretty sure you'll find it here. Word of caution, though: Most places charge a cover fee (anywhere from $5-$20).
Dress Code: Dress code is fairly casual for the guys (think JCrew sweaters and jeans), but the ladies tend to dress up a little more. Definitely leave your nice shoes at home, though - they'll just get beer all over them.
This is a nice place during the day, but at night it is more fun. Around an indoor market you'll find shops that are opened until late and lots of bars. This place has a very cosy, European feeling, a bit like what you'd expect from London or Dublin, great Irish pubs. It is completely different than nightlife in NYC, but it's definitately as much fun!
If you're interested in dancing and bar hopping, try the area around Faneuil Hall. Start at The Rack (therackboston.com). Offering food, drinks and all the pool you can handle, you may even see local and national celebrities hanging out. Most Thursday nights you can also catch Mark Morris and the Catunes, one of Boston's best musical acts. There are Irish bars like The Black Rose, Hennessy's and the Green Dragon Tavern.