I saw on television today, that yesterday...the grand opening for MOMA was free...but beginning today, it will cost $20 to go in. I don't know if they have any special prices...but I'm sure that $20 is worth it...besides, they've got to PAY for that new building!
The Metropolitan Museum of Art has a suggested admission. You can give as little as you want and still enter. I don't think the Museum of Modern Art has that. Each museum is different, especially in NYC.