The best for you and your location is Rattle N Hum on 33rd between 5th and Madison. Great selection of local and national craft brews as well as 3 or so cask ales on tap.
Gingerman is another option though their selection is not as good and I personally don't like their crowd.
Local beers-Anything Captain Lawrence, most Sixpoint and Brooklyn of course. Some limited Chelsea offerings are good as are some Bluepoint ones.
"Micro brew". Haven't heard that one in a while. I think most places have migrated to the term "craft beer". Anyway, not sure what's good craft beerwise in the 40s-50s, but a bit further south into the 30's are two of the best places in the city:
Rattle N' Hum-