I live in NJ. For 2009 I worked part of the year in NY, the rest of the year in NJ. Do I file state taxes in NY for just the employment I had in NY?

Yes, on the NY tax return report income earned live in NY. You are nonresident of NY.
On NJ return, claim your worldwide income. Claim credit for taxes paid to NY. Your U.S. Tax Return: Working or Living in Two or More states (http://taxipay.blogspot.com/2008/06/working-in-two-or-more-states.html)

On the NY non-resident return you must report your entire income AND your income that is from NY sources. You report your entire income so that you are put into a tax bracket commensurate with your total income - then that bracket is applied to the portion of your income from NY. The result is you pay taxes to NY only on your NY income, but possibly at a higher rate.