MOMA: My wife and I were alone with The David for a few minutes at The Accademia by getting there very early in bad weather & I was alone with the Turners at The Tate for a good 20 minutes! (they weren't actually open yet..this caused some problems..a story for another time).
The same goes for MOMA..get there when they open and preferably not a Friday and you should be fine. And the when it gets crowded, the people watching is world class too. And check the film schedule-you're entitled to free tickets with admission.
When you go to ICP: Yum Thai at 129 W. 44th (between 6th and 7th) is cheap and very good as is the hallal chicken stand on the NW corner of
5th and 44th. The fallafel stand on southeast corner of 46th and 6th is also excellent.