Kimberli is absolutely correct, you will pay income tax in the state where you work. I am not a NY resident, but I do live in PA, and the East Coast is a big change from my former life out West. You should spend some time researching, but if NY can rip tax money out of your pocket, it will, regardless of where you claim residency. Keep in mind that taxation rules are different in The City than in the rest of the state, so be careful to look at the correct information. We have so many levels of taxation that it makes my head spin. State, County, Township, Borough, etc... Most of the townships even have "occupancy tax" that ranges from a few bucks, to a few hundred dollars per year...regardless of whether you work or not.
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