Hmm...so after you go to New York for a few days, you're then going to New York for another 10 days? Oh, I get it, you're going to New York STATE for a few days, but then going to New York, New York for 10 days.
Must sees would include all the "normal" touristy things, Empire State Building, Statue of Liberty, Chrysler Building, Ground Zero (unless you're Ahmadinejad they'll let you visit
) etc. If you like TV, watching a taping of The Late Show is lots of fun, contact CBS NOW to try and get tickets. Central Park, the theatre district, Washington Square, the ports, 5th Avenue, Rockefeller Center, the ice rink, the museums (MOMA is a big attraction), Greenwich Village, man, ten days is not enough.