Kinokuniya: Japanese book store (english and japanese books, anime, manga, stationary supplies, arts and crafts etc). There's a cafe (cafe zaiya) on the 2nd floor with delicious food and desserts. it's also right across from Bryant park.
and in Bryant park there is a large central library. It's huge but you cant borrow books out of the library. Only use them inside.
a few blocks away there is...
BookOff: used Japanese book store. Used Japanese and English books, video games, dvds, cds, and game systems.
Museum of Natural History/Planetarium: They have awesome shows (like the space show) and other displays/exhibits.
St Marks have a lot of interesting shops (also some sketchy ones), lots of restaurants and places for a quick bite to eat. Next to this block/street there is Panya: Japanese bakery, Sunrise mart: small Japanese supermarket, and down the street there is Otafuku: a small Japanese okonomiyaki, Takoyaki place. (<- its basically a hole in the wall food stall/restaurant. Also in the St. Marks area there is an awesome restaurant for yakiniku/Japanese BBQ called Gyu-kaku (its a bit pricy).
In Korea town there is food court called Food Gallery 32. There's Korean food, Japanese Food, a mix of them, and dessert.
Shake Shack: Awesome burgers. 100% beef. (or mushroom burger). Depending on the location there will probably be LONG lines.
Central park is huge so pick a place to enter.
Bon Chon for some fried chicken and more.
Pio Pio: Awesome Peruvian food. Only been to the one in Hell's Kitchen though.
The Counter: Custom Burgers. Delicious~ it's also right next to...
Ruby Tuesday: a bit pricy but delicious food too.
Mitsuwa: Large Japanese supermarket (food court + desserts) in Edgewater New Jersey. 30 mins away with shuttle bus from port authority (NY). Best time to go is when they have food fairs/festivals. But it's still nice to go when there isn't a festival. There are other shops in the complex as well like a Japanese bookstore.
Argo Teas: nice teas (I only get chocolate chai). It's like starbucks but instead of coffee they serve various teas.
Nintendo World: (formerly known as the Pokemon center) ... if you're into games and nintendo stuff.
Minamoto Kitchoan: I tried it once. Japanese Wagashi/sweets. subtle flavor but delicious.
that's all I can think of so far.