Sucks that it's cold - if it was summertime and you were meeting people, most can get on the roofs of their apartment buildings and enjoy the sunshine. I'm not sure of winter things to do (it might be cold enough to skate at Rockefeller Square, I guess), but these are some of my notes having been there a few times (usually in warmer weather):
Avoid Times Square unless you want to walk in the parade of all the other tourist yuppies.
Check out the High Line Park on the West Side - cool concept, good views, neat area.
Battery Park is fun, grab an outdoor beer there.
Central Park is enormous and full of things to do.
If you've never been, the American Museum of Natural History is a must.