I lived in NY for 9 months in 2009 and have a W2 from there. I moved to Hawaii the ending of September 2009 and also have a W2 from Hawaii also. My questions is what state do I file my income taxes. Do I have to file state income taxes in both states?

Yes, file NY and Hawaii tax returns.

To clarify - you file as a part-year resident of NY and as a part-year resident of HI. Both states will require you to repoort your full income for the year, but as you work through the forms you'll see that in the end you pay NY tax only on your NY source income, and HI tax only on your HI source income.