I would say spend as much time checking out the Lower East Side  and definitely Williamsburg, Fort Greene and even Bushwick depending on how interesting you want your experience.

Here are some highlights from around town.

BBQ in Brooklyn Fette Sau - http://www.fettesaubbq.com/

Schiller's Liquor Bar - Awesome cocktail spot and casual dinner in the LES. http://www.schillersny.com/

Brooklyn Museum<http://www.brooklynmuseum.org/> – The museum has been recently renovated which makes it a treasure to visit plus it has its own subway stop, so easy to get to.

Milk Bar <http://newyork.seriouseats.com/2009/08/vanderbilt-milk-bar-brooklyn-prospect-heights.html> for decent coffee and breakfast before you go – it’s not too far from the Brooklyn Museum.

MOMA <http://www.moma.org/> –We broke up our visit with lunch at the too cool food hall on the second level, there’s a great selection of local wine, food & beer (there’s another on the 4th level which was underwhelming – avoid that). Like the Brooklyn Museum, it’s closed on Tuesdays.

The Frick Collection <http://www.frick.org/> –I found it really interesting as the collection is more than just art on a wall. This dude had some serious nous in the taste department so the collection is more about his actual digs which are off the hook.

SPiN New York <http://spinyc.com/> is the first dedicated table tennis nightclub in Manhattan. It’s fully licensed and has a restaurant as well.  Featured in the final episode of Entourage.

Ippudo NY<http://www.ippudo.com/ny/> for ramen noodles in the East Village, though best to come before 7pm or after 10pm than endure an hour wait. The vibe is Zen.

Spunto <http://www.spuntothincrust.com/> for pizza in Greenwich Village was relatively new, cheap & rated well by Zagat.

Amy Ruth's Restaurant <http://www.amyruthsharlem.com/> for fried chicken, waffles and corn cakes in Harlem. You can combine this with a visit to the Apollo Theater as well.

The most authentic slice I had in Brooklyn was at Roma Pizza<http://nymag.com/listings/restaurant/roma-pizza-and-restaurant/>. The fresh mozzarella pie is by far the highlight.

Best coffee I found was run by an aussie bloke, near 38th and 6th. Counter Culture Coffee <http://www.counterculturecoffee.com/>. They also do cold brew (yeooow).

Joe the Art of Coffee<http://www.joetheartofcoffee.com/index.htm> for coffee near Washington Square Park was excellent though I found there was usually no seating whatsoever due to the wifi connection being used up by laptop zombies. Morandi <http://www.morandiny.com/>, in the same neighbourhood had a killer wine list and good, honest Italian food. Best to book ahead.

Try and get to Brooklyn! There is a lot of really good food and cocktail spots. There is also the Brooklyn Flea Market on Saturdays. All of which are just a couple of subway stops from where your are staying.

Food:

Five Leaves Restaurant A great breakfast/brunch spot.

Tabaré 

Cocktails:

Maison Premiere This Place has $1 oyster happy hour and amazing cocktails!

There are a number of great shops and eateries all over Williamsburg, give it a shot!

If you haven't been to the High Line Park, it's definitely worth a visit. Walk from Chelsea (New York) along the High Line down to the Meatpacking District and end up for cocktails at the The Standard New York, or lunch/dinner/brunch at Pastis, or walk up to the Chelsea Market to explore with other foodies.

Hopefully the weather will be great and you can enjoy the great views of the city and Hudson. Cheers!

Hi, Diego,

Not entirely sure what you're looking for--maybe if you list a few things you like to do ordinarily (museums, music, etc.) I can be more help. That said, here are a few things to get you started:

You might like  Harlem It's had a lot of re-growth in the past few years and is a very exciting place. Check out  Ginny's Supper Club for great music and  Sylvia's for incredible soul food. 

It's the perfect time to check out the  Brooklyn Botanic Garden which is one of my most favorite places on earth. While you're in the area, check out the  Brooklyn Museum which always has something interesting going on. 

One of the best and often totally overlooked museums in NYC is the  Rubin Museum of Art which features mostly Asian art. It's one of my favorite places in the city and I love their cafe. 

I haven't been to the  American Folk Art Museum yet (I don't know how I haven't been) but everyone I know says it's amazing. 

Have a great time!!!

Go to New York Transit Museum in Brooklyn  it is a fascinating display and story of how the subway was built back in late 1800's  thru  modern times.

There are a number of Free Walking tours to take advantage of. If you like food, there are walking food tours of different parts of city. You can find these by googling them. 

If you're mostly in midtown west, I'd strongly suggest Hell's Kitchen as a place for great, off-the-beaten path eats.

Here're some great restaurants in that neighborhood:

• Becco: Lidia Bastianich's Italian restaurant, big pre-theatre scene. Has a really great all-you-can-eat pasta special.
  
• Nook: cute, tiny BYOB restaurant with great diverse offerings
  
• Momofuku Milk Bar/ Má Pêche: try the crack pie. Ma peche has a new tapas menu which is supposed to be fantastic. Also would suggest their cocktail bar  Booker and Dax at Ssäm (E. village) which has great molecular gastronomy drinks (or any Momofuku Noodle Bar/ Momofuku Ssam Bar)
  
• Island Burgers and Shakes: hole in the wall with great burgers. Also try  Shake Shack but that's far more touristy (still great!)
  
• Don Antonio by Starita: really great pizza, one of which has a deep-fried crust (seriously). Also on city's best pizza list:  Co. (Chelsea) and  Motorino (E. village: my personal favorite but it's a bit of a trek).

Cocktail bars:

• Raines Law Room (flatiron): fun speakeasy type bar
  
•  Pouring Ribbons: in the middle of nowhere, but great drinks (alphabet city)
  
• Not sure if the weather will be great enough for them to be open but I'd totally suggest the outdoor bars the  Frying Pan (Chelsea) and the  West 79th Street Boat Basin (UWS). They have gorgeous views on the Hudson and they're especially nice for a drink during the day.
• The  Empire Hotel has a nice rooftop bar but it's a little touristy 
  
• You've already done Eataly but their  Birreria is also really great and has a nice view.
• The Biergarten at The Standard is also a little crowded but super fun, and it's right by the  High Line Park which is great if you haven't been yet.
  

Other activities:

• Bryant Park/the New York Public Library
• MoMA
• Central Park Zoo/Central Park (cherry blossoms are out at that time which is very pretty)
• High Line Park (as previously mentioned)
• Frozen yogurt (ridiculously trendy right now, there's one on every corner: 16 Handles is an especially popular one. It's silly but definitely a NY "experience")
• Tribeca Film Festival will be April 16-27. Easy to catch cheap screenings all over the city of new films and often the cast/director comes for a question/answer session (
• Broadway shows ("If/Then" just came out, with Idina Menzel ["Rent"/"Wicked"])

Hope this helps!

Have a great trip!

Jennifer

Try Angel's Share and  Booker and Dax at Ssäm in the East Village for good cocktails, and The Standard - East Village is good for a drink and a view.

Baohaus may look dirty but it has amazing reviews and the best Chinese sandwiches around.

Warby Parker has a showroom in their office.

Peking Duck House - Midtown Location

This beautiful, reasonable and fresh Chinese restaurant is unique and remarkable. It's as authentic as you get . . . no salt, no MSG. Everything is marvelous but if you like Peking Duck, this ranks among the best in the U.S.

The Cloisters in Upper Manhattan are beautiful.  You can then have a Gospel Brunch in Harlem.

hi there, venture out to East Village! great area or perhaps even Williamsburg/ Bushwick if you want to get out of the touristy places. do Lafayette, ACME, Cafe Mogador or Cafe Orlin for food. all delish and reasonable. get a citibike and ride around town. see some art exhibits in chelsea! plenty of artworks to visit. get some " Big Gay Ice Cream Shop", Crif Dogs or eat at Caracas Arepa Bar. hop into The Immigrant for drinks or Experimental Cocktail Club. Apothéke is a cool place to visit for dancing in chinatown.

If you're a fan of poetry/spoken word, check out Nuyorican Poets Cafe. One of my favorite places in the city!

You should definitely check out the Murray Hill area (east 33rd ish street and 3rd Avenue) they've got some amazing/quirky bar restaurants for the night time. St. Marks Place (2nd Ave and 10th-5th street) cheap food and interesting melange of people. While you're there, get some delicious fries at Pommes Frites. Midtown Manhattan gets very fun during the weekend (just stay near 3rd ave and 50th-59th street) for food and bars.

Try walking the High Line Park. Or visit Coney Island if weather is nice- before the crowds get there in summer. maybe some galleries too.

Prune

Go to High Line Park and take a long walk if the weather is good.

Eataly

High Line Park