Don't waste precious little time going to the MOMA. last time I was there; last year; it was a total joke-throngs-no hoardes of people just moving through the galleries. this is no way to appreciate art. stick with the private galleries. pick up a copy of photograph magazine-no just subscribe to it as it covers most of the major stuff in the usa.
here's a little list for you....
Museum of the City of New York
Some of these are in midtown-the rest downtown where the real people hang out, there is a huge collection of galleries as someone mentioned on the west side of town. there is ALWAYS some great art in the big apple and if you have limited time make sure you check the hours of operation. and forget mondays
summer schedules may differ...