I lived in NYC for 10 years. I've found that people mostly want to have their photos taken at various places, so these are on my list. The things that seem to satisfy my visitors the most were:
Times Square. Better at night with the lighted billboards. If you stay at a hotel in this area, you can also get the day and night photos easily. Times Square at night always overwhelms out-of-town visitors. My mother was almost catatonic, so it will please your teenager.
Empire State Building. It's the best view in the city--north, south, east, and west. Again, timing is everything. Go when there is still daylight, and try and time it as the city gets dark. If you can't, go in the morning before the lines get long.
Rockefeller Center and
St. Patrick's Cathedral.
Staten Island Ferry. Great views of Statue of Liberty and lower Manhattan. If you time it right, go in the evening while it's still light, and cross back at dark when the City lights up. You can also opt to do the tourist ferry that goes all around Manhattan.
Having a picnic in the
Sheep's Meadow in Central Park. Go to some deli and buy supplies. Enter around Columbus Circle. My visitors enjoyed this experience a lot. The casual picnic gazing at tall buildings and people-watching was enough. Walk over to Bethesda Fountain and watch the boaters in the pond. If you've been walking a lot, it will also give you some time to rest.
A teenage daughter will also enjoy a trip to Serendipity on the Upper East Side. One goes for the desserts. Jackie Kennedy-Onassis used to take her kids there.
http://www.serendipity3.com/
Walk across the
Brooklyn Bridge. Everyone likes to have their photo taken there, and the view from the Brooklyn Heights promenade is lovely. You can combine this with a walk through the labyrinth of narrow, chris-crossing streets around Wall Street, and go look at the construction at the World Trade Center site.
https://maps.google.com/maps?q=mulberry ... -3.93&z=21
https://maps.google.com/maps?q=mulberry ... -36.9&z=18
Having dinner in
Chinatown / Little Italy in the evening (Mulberry and Hester streets). One does this mostly for the outdoor dining / street experience. The tourist gift shops are generally cheaper than those around Times Square.
https://maps.google.com/maps?q=mulberry ... 9,,0,-0.87
While in Little Italy, walk over the old
Police Station building at Centre and Grand--one of the loveliest and most-overlooked buildings in the City. I've always been partial to Vincent's at Hester and Mott. But there are several other long-time restaurants, and good ones along Mulberry Street.
http://www.10best.com/destinations/new- ... alys-best/
Vincent's
http://02de1be.netsolhost.com/fame.htm
https://maps.google.com/maps?q=mulberry ... 2,,0,-8.91
Taking the subway out to
Coney Island and lounging on the beach in the afternoon. Go to Nathan's hotdog place. There's not much else to do at Coney Island than lounge on the beach and eat at Nathan's. The subway trip out there is interesting visually. Get up early and go in the morning. If you and your daughter could care less about going to the beach, then nix it for something else. My visitors were mostly from places that didn't have beaches, so they enjoyed it.
https://maps.google.com/maps?q=mulberry ... -8.54&z=18
Taking in a
play or musical in the theatre district. Buy tickets at the TKTS place in Times Square. Keep in mind you are entertaining your teenager and not yourself. A serious play might not cut it.
http://www.tdf.org/TDF_SupportPage.aspx?id=97
You will do a lot of walking, so be sure to divide activities up to allow breaks.
Wear your most comfortable shoes. People who don't live in New York City are not used to doing so much walking, so you will be tired.
Wear your most comfortable shoes. Also remember that in the summer, the subway stations are hotter than hell. The train cars are air-conditioned, but you have to wait in sweltering tunnels until they arrive. Another trick that might help. You might try changing shoes during the day and it will relieve stress on your feet. So take two comfortable pairs of shoes. Don't haul around a backpack or a heavy camera. It will kill your back and neck. In the hot summer, you will sweat, so drink lot of fluids. Getting dehydrated will wear you out, and you will become a bummer to your daughter. Don't let your wife or daughter wear flimsy sandals. Don't do it. They will complain all day about how their feet hurt. Plus, in crowds and on mass transit, people might step on their toes. No purses with long straps either. Preferably, no purses.
For long jaunts fast, take the subway. For short jaunts, take a city bus. The buses allow a side benefit was mini-tours because you can look at things while the bus moves about. Buses are also less disorienting than subways for newbies.
The double-decker sightseeing buses are fine for the first day because they move slowly through the City and allow visitors opportunity to gawk at things. They stop at all major attractions, and come regularly, so you can get on and off for as long as you want, and then continue when then next bus comes. You can also opt to not get off and just ride around getting a feeling for things, and then come back to those you want. Young people see them sort of like an amusement park ride.
Also, if you are in need of public bathrooms. Major hotels, hospitals, Barnes and Nobles, Borders, Starbucks, and Virgin Megastores are good places for clean bathrooms, or try and time it around eating in restaurants.
You don't always need to eat at fast-food places, or fancy restaurants. Neighborhood diners are good for that, and that's where New Yorkers eat.
A note on the
Statue of Liberty. It's okay to go to the island and gaze at it. However, the trip to the top is long, and mostly disappointing because it's very cramped, and the windows in the crown are very small, and you have to bend over to look out of them. One gets as good as a view of the statue from the Staten Island Ferry.
The
South Street Seaport is mostly a letdown.
The
Intrepid Sea and Space Museum will probably bore your daughter. Wife and daughter will probably rather walk down Fifth Avenue looking at store windows instead. Of course, you will be bored.
Save the museums for last after you have already hit the major sites. They are more expendable if you are running out of time and energy. The museums take up a lot of time to go through, and may be better left for a later trip. Teens tend to get bored in museums.
An odd little sidebar. My visitors always seemed to enjoy taking taxi cabs. It's part of the experience, so think of it like an amusement park ride. You can always take other forms of transportation during the day, but at the end of the day, when you are tired, opt for a cab ride back to the hotel. My 18-year-old nephew thought taking cabs was fun.
The other thing is your teenager might also enjoy a horse-carriage ride in Central Park. It's more extravagant, but something she will remember. A boy might not care so much, but girls have this fairy princess vibe inside their heads, even if they don't admit it.
Small things. Eating at a sidewalk vendor stand. Eating at a busy sidewalk café. Seeing the crazy end-of-the-world soapbox types in Times Square. Feeding the pigeons. Seeing a rat running along the tracks in the subway. All of my visitors seemed to like going to the
FAO Schwarz Flagship toy store on 5th Avenue. Mostly because they haven't seen such a big toy store in all their lives. It's good for a quick looksee and it's close to St. Patrick's Cathedral and Rockefeller Center. It's in the General Motors Building at 58th and Fifth Avenue.
http://www.fao.com/shop/index.jsp?categoryId=3810526
Finally, keep a journal of all the places you go, because over the years, your daughter will start to forget some of them. Attractions, names of restaurants, etc. It will all fade into a blur. If you are resourceful, you might Google map them and make a scrapbook with the photos showing the places and addresses--however minor. Include ticket stubs, playbills, transit maps, takeout menus, etc., as well as the photos your take. This might be a job for the wife.
The thing to remember is you are giving your daughter a lifelong experience and memory, which is a better gift than anything physical you can give. You might be surprised what her favorite memory will be.