Sixpoint beers are on tap at a lot of places around the city, not too hard to find. Check beermenus.com to see who is pouring them. Pretty much everything they make is amazing Brownstone is a favorite, but you can't go wrong with Sweet Action (a blonde), Bengali Tiger (IPA), or Righteous Rye (Rye beer).
I can echo the Blind Tiger reccomendation, but if you can try to go early afternoon or at least arrive before everyone gets out of work, it's a tiny place and it tends to get packed.
McSorleys is a trip, oldest bar in the city, interesting vibe, but be warned - it's anarchy at night. Go for vibe, not for great beer.
Ginger Man has very nice choices, but it's in midtown and get's packed with the suit and tie crowd at happy hour.
Swift Hibernian Lounge has a great selection and very cool vibe.
Pony Bar - great spot - sometimes they'll give over all their taps to a single brewery.
Queens:
If you can get to Queens the Astoria Beer Garden is the last of the traditional German style beer gardens in NYC although apparently someone did open another one nearby that is also supposed to be nice.
In Brooklyn:
Spuytin Duyvil - quirky little beer bar with an epic selection of Belgian beers and good smattering of others, mostly bottles
Muggs Ale House - standard bar with great tap selection
Brooklyn Brewery - only open during happy hour on Fridays from 5-10 and Saturdays from 12-5. Tours on Saturdays, no appointment needed. Fun scene, they put out picnic tables and you can order takeout from local restaurants and gawk at the ridiculous hipsters. Best beer deal in the city 6 glasses for 20 bucks and you get one free with an AHA card if your a member.
Bierkraft - mostly a retail establishment, but they do have tables where you can sit down and enjoy a pint and one of their excellent sandwiches. They have somewhere around 700 different bottles from around the world plus a dozen beers on tap and 3 casks of real ale which they'll put in counterpressure filled growlers for you. My favorite business in the world.