Cool in Brooklyn for me means eating at Grimaldi's Pizzeria in DUMBO and then walking over the Brooklyn Bridge to Chinatown New Yorkand getting some dim sum, walk up Canal St. and check out Little Italyand then walk off all you've eaten by walking the Village.  My fav street is Hudson and you can take a left right off it and see the Hudson.

I really like the Brooklyn Flea Market, for people watching, too.  But check dates in winter -- it might be closed.

A day trip in NYC sounds great. :) 

If you enjoy walking around and photographing cities, then I'd definitely recommend High Line Park. You'll get some great views of the city from above. Grab a coffee/tea and dress warmly if you go. There are fun cafes/restaurants around Chelsea (New York), which you'll be near. 

Depending on how early you get in, seeing the tree at Rockefeller Center could be fun (the earlier, the better...as it'll be crowded). If you want to escape the crowds, head toward Columbus Circle to walk in Central Park and to the Upper West Side. If you want to venture uptown more, Harlemaround West 125th street, has a lot to offer in terms of history/culture with places like Apollo Theater and great food, as well! 

If it's chillier and you want to spend some time indoors (on either the Upper East or Upper West side), check out great museums like the Museum of Modern Art, Solomon R. Guggenheim MuseumThe Metropolitan Museum of Art American Museum of Natural History. 

For awesome views of the city and in Brooklyn, head over to Brooklyn Bridge park. From there you can venture out to popular areas like DUMBO Brooklyn Heights Park Slope Greenpoint and Williamsburg

If you'd like tips for fun events/ticket deals that might be happening this weekend, check out: http://www.theskint.com/ongoing-events/ and http://www.nycgo.com/

I always enjoy the West Village in NYC and particularly love either eating at or imbibing The Marlton Hotel.

If you want to experience Brooklyn and lower Manhattan by foot, here's a promenade-to-promenade path you might take. Start in Brooklyn Heights and walk along the East River promenade to enjoy the lower Manhattan Skyline. Make your way to the Brooklyn Bridge and cross it on foot. Then head south through City Hall Park and cut across Vesey St all the way to the World Trade Center. Then take Liberty Street to the North Cove Marina and head south along the promenade down to Battery Park. Finish off at South Ferry/Terminal where you can catch the R train back to Brooklyn. Or walk a block north to the Bowling Green to see the Charging Bull and catch the 4/5 train back to Brooklyn.

NYC is always exciting and fun no matter what you do! I've been getting some good ideas and discounts on things to do from an app I downloaded called GOLDSTAR. I have my area set for NYC and it suggests things and offers discounts! I don't know what you consider "cool" but there are many things that have piqued my interest! Good luck and have fun!

If it is the first time and if you want do the cliché of looking at the Manhattan skyline from up above, choose the Rockefeller Plaza over the Empire State Building . The view is better and in the Empire State Building, there are scammers for tourist looking people...

Instead of waiting in line @grimaldis go to @julianas for pizza instead. Patsy Grimaldi is the original owner of grimaldis and now runs julianas. After you enjoy your pizza you can head to the @brooklyn bridge park or cross the Manhattan bridge and wander around chinatown.