Get the best tickets you can afford to a great play, something like Phantom-I'd get them in advance.
St Patrick's Cathedral.
I like to walk around, depending on when you go... I enjoy sitting in an outdoor restaurant drinking wine, having a caprese salad and people watching.
If you plan ahead you can get tickets to TV taping, back in the day I took the kids in my family to see the taping of Cosby and Kate & Ally. A lot of them are in Queens, you can't get there.
I really don't do public transportation, but if you get in a cab make sure they reset the meter-LOL. It might be a good idea to stay away from 3 card monty on the street.

Try to blend and not look like a tourist, people are great about answering questions, just not stupid ones.
Get coffee and a bagel, eat some really good Italian food, have a drink at the Mariott Marquis at night and see the architecture-the Chrysler building will take your breath away from up there.
Have fun.
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Loving life in the Village of PattyLand
Y'know that part of your brain that tells you "ENOUGH IS ENOUGH!" I think I'm missing it.