There’s a possibility that Piper Family might be able to swing a month living in NYC in a year or too - not a short visit or a business trip, but hiring a flat and just hanging out for a month.
What would Dopers recommend as must- sees, must-dos? Or, what about things that tourists don’t normally do because pressed for time, but New Yorkers might do?
Any and all suggestions welcome.
Central Park. 
What time of year?
The best thing is that you’ll be able to take your time. Not trying to squeeze it all into one week.
What are your interests? History? Art? Sports? Food?
Live in Brooklyn!
the Brooklyn Museum, the Botanic Gardens, Prospect Park (the equal if not the better of Central park), West Indian Day Parade, the Brooklyn Public Library/Grand Army Plaza, Sunset over Manhattan as seen from Brooklyn Heights, The Transit Museum, Junior’s Cheesecake, Brooklyn Chinatown, New York Aquarium, the Cyclone rollercoaster, Cyclones minor league baseball, Little Odessa, The Mermaid Parade, Nathan’s Hot Dog Eating Contest…
Brooklyn!
Yes, what time of year, and what types of things do you enjoy doing where you live now?
Oh, and are there children in your family, and if so, how old?
I’m going to have to say ‘fall in love’, of course. What else? It’s the best that you can do.
If you are into ethnic food there is a Chinatown in Queens that has some of the best authentic chinese food in the country. There is also a Little Italy in the Bronx that is bigger than the one in Manhattan.
Only if you are caught between the moon and New York City
New York is an amazing place for shows, not only Broadway, but famous artists and bands. So, start looking now as to what’s coming up and when you can buy the tickets. Some Broadway shows sell well in advance, you may be able to buy decent seats now.
If you like classical, Lincoln Center and Carnegie Hall will release the 2013 season in the fall. For Jazz, there’s the Blue Note, Village Vanguard Irridium, B.B. King’s etc. Also, MSG/Radio City Music Hall/Beacon Theater have a common schedule/sales site.
There’s just so much happening there.
If you haven’t already arranged your rental… be sure that it is near a subway stop. Even 3 blocks can be too far away (e.g. east-west blocks in Manhattan are long, almost a 5 minute walk). You will be using the subway all the time I’m sure.
If you’re into history, check out Forgotten NY (there’s a website and a book) and consider exploring NYC hunting for relics from its past.