What day of the week are you planning to be here? If it's a weekend, particularly Sunday, there will be plenty of on street free parking available.
And please do not just put "stuff" in your trunk and then walk away on the street. It's a general rule of city parking, in my book, to drive to another spot elsewhere, after placing something in the trunk. And as the Christmas holiday season approaches, the odds of a trunk breakin increase.
Having said that, nearly all of Manhattan is very safe, as is most of NYC.
And be aware that there is a NYC section on FT as well here:
http://www.flyertalk.com/forum/forumdisplay.php?f=465
So enjoy your time in wonderful NYC!
Mark