I take the subway 24-hours a day without incident (and I'm female). Just don't flash money around.
Financial District is kinda dead at night but the subways are fine.
I second the opinion on Wollman Rink vs. Rock Center - RC is way too expensive and they limit your time and lines are LONG!
Just walking through the Park in fall/winter is very pretty.
NYC is a lot safer than it used to be. Just keep your eyes open
Cabs from JFK to anywhere in Manhattan are flat fee of $30 + tip and tolls. From Manhattan to JFK there is no flat fee but it will be around the same price, maybe slightly more. To/From lower Manhattan it will take about 45 minutes.
Unless you like massive crowds of tourists, avoid Rockefeller Center. Also, at Rock Center, be aware of pickpockets - they come out during the holidays.
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I wish I were 1,000 miles away