I briefly skimmed the other threads about NYC. Forgive me if I repeat something already mentioned. I can give provide some info on stuff I like in NY.
For art, the most concentrated neighborhood for art galleries is not Greenwich Village, it’s Chelsea.
Williamsburg in Brooklyn has more up and coming art galleries, and Chelsea has more galleries for more established or mid-career artists. A great internet guide for art galleries and openings is dks.net.thing. The regular gallery hours are in the day, and the openings are usually in the evening except on weekends, they may be in the afternoon.
Williamsburg has a small hipster scene that you may get a kick out of. Cool bars, clubs, cafes, and shops. There is only one small strip of it on Bedford. Then there are other cool places more interspersed.
I think two overlooked and underrated art museums in NY are the Brooklyn Museum of Art that often has better shows (edgier and more interesting contemporary art) than the Metropolitan and MoMA. Also there is PS 1, which was originally a public school (that’s what the PS stands for) that was donated to MoMA. which is in Queens. Most of the time has really great contemporary exhibits where I’ve seen some of the best contemporary work. The space itself is really cool because they preserved the look of the school. Even the bathrooms and staircases are something to look at.
Another underrated museum that I have only visited once or twice but was interesting was the Folk Museum which is next to MoMA. If you are going to see MoMA, you might as well see the Folk Museum as well.
NY also has some great off off broadway shows. The Village Voice has a decent section for theater, and they have a website.
If you’re going to visit the Metropolitan Museum of Art, two of my favorite sections are the Temple of Dendur and the Costume Gallery in the basement (often has great exhibits).
If you go to Chinatown, don’t eat at Joe’s Shanghai, though the food is decent, it’s only average for the area and is overpriced. It’s only a popular restaurant in Chinatown because it’s in a lot of guide books (tourist trap). The best Chinese food I’ve had in Manhattan is at Grand Schezuan which is not even in Chinatown. I think there are two locations, one in midtown Manhattan and the other on St. Marks Place downtown.
Last time I counted there were four Chinatowns in NY. The best known one is the one in Manhattan, but I think the one in Flushing, Queens is more authentic and less touristy. It also has better restaurants. Both have a different feeling and different populations. The Chinese in Manhattan’s Chinatown are more economically disadvantaged, and the ones in Flushing are more middle class. There are also a lot of Taiwainese and Koreans there as well. Main Street is the main drag in Flushing. Look in one direction and there are Chinese and Taiwainese shops and restaurants and the other direction is Korean. The two other Chinatowns are in Brooklyn, btw.
The Chinatown in Manhattan does have an interesting ice cream place called the Chinatown Ice Cream Factory that has interesting flavors such as Lychee, Longan, Green Tea, Red Bean, etc. Don’t get me wrong, some of the restaurants there are very good–ironically, some of my favorite restaurants in Chinatown are not Chinese but Malaysian and Vietnamese. I wish I could remember the name of this really great one.
I think Queens in general is very underrated. Jackson Heights holds the title of the most ethnically diverse neighborhood in the world. The best Indian food (others may disagree) is at the Jackson Diner in Jackson Heights.
There is a curry row (bunch of Indian restaurants) in Manhattan that is popular, but the food is very mediocre but cheap.
There are a lot of great shops on Broadway in Downtown Manhattan. Two fun stores that I think you might like are Pearl River Mart (for Chinese stuff) and Yellow Rat Bastard (that young adults and high schoolers might like).
You might also want to check out Lincoln Center on the Upper West Side, good for opera (expensive of course) and other shows. I’ve never been that keen on Broadway, but some people must like it.
There is also Little Italy which is just north of Chinatown if you are in the area. Though others may disagree, I still think that Lombardi’s has great pizza. There are a ton of brick oven or coal oven pizza places, but Lombardi’s has the best toppings. Also for pastries, I would recommend Ferrara Cafe in Little Italy. Also Veniero’s in the East Village is also well known for good pastries. And if Veniero’s is too crowded, there is DeRoberto’s across the street.
As far as bookstores go, Strand’s is well known and huge, but another noteworthy one in NY is St. Mark’s Bookstore. Smaller but has a great vibe and selection of books. My favorite bookstore in NY.
Also for the season, (if you are into this type of thing) check out the window displays at some of the large department stores like Bergdorf Goodman and Barney’s.
I wish I could say more, but I have to go to sleep.