I used to live in Manhattan and Brooklyn. Whenever I go back to NYC, I try to stay at an actual apartment. As long as you're careful not to fall for scams, Craigslist and Airbnb have a listings for entire studios/apartments in very nice areas like the Upper East Side, Upper West Side, etc. I have found and stayed at two good, clean, spacious and quiet apartments conveniently located in the Upper East Side, very close to the subway. They were $150 per night, and bigger than any of the hotel rooms that cost the same in Manhattan. (The ones costing under $100 are not as nice, I have to say.) With the money I saved staying in an apartment instead of a stuffy characterless hotel room, I splurged at Peter Luger Steakhouse (make your reservation NOW, otherwise you'd be stuck with an awkward time), Beard Papa (cream puffs to die for!), Zabars and Fairway Market. The Union Square farmers market is a good excuse to pick up some fresh bread and other picnic foods to eat in the area.
Central Park is nice, but do check out the High Line. It's fabulous, and absolutely free! When you and your daughter get hungry, go inside to the former Nabisco factory -- now known as Chelsea Market -- for ice cream/milkshake at the Ronnybrook Farms store. Ninth Avenue Espresso has also set up shop inside Chelsea Market. Within walking distance of Chelsea Market is Sea Thai, a very good Thai restaurant that has an outpost in Brooklyn's Williamsburg neighborhood as well.
People always talk about going to the top of the Empire State Building, but it's crowded and you basically have to wait in two lines. Double-annoying. One line to buy the tickets if you hadn't bought them online ahead of time, and another line to wait for the elevator to go up to the top. Whenever I had visitors, I'd take them to the top of the Rockefeller building instead. It's called Top of the Rock, and the plaza below is prettier besides. Check if you can buy tickets online in advance to save you time. It's only a dollar or two more than the Empire State Building, but more beautiful.
A walk across the Brooklyn Bridge is nice. If you walk to Brooklyn, look for the Jacque Torres chocolate shop as a reward to yourselves.
One "secret" I always share with visitors is there is a free ferry that goes between Manhattan's Wall Street area and Brooklyn's Red Hook area. Red Hook used to be a little on the shady side years ago, but with the establishment of many artist studios, cute restaurants and boutiques and Fairway Market, it's much better than it was. The Red Hook Fairway Market has an outdoor eating area that is perfect for watching the sunrise and you get an unobstructed view of the Statue of Liberty. (Get lobster roll or smoked salmon bagel or any other bagel at the Fairway deli!) During the weekends, the ferry is free. During the weekdays, you have to furnish proof of a $5 Ikea purchase (I believe, but double check). If you walk around the Wall Street end, there's a very special, tiny, cobblestone lane called Stone Street. It's like being transported to a European city, with cafes and restaurants flanking each side.
Sorry for the long post. I am very excited for you and your daughter. Have a great time!
