I live in the state of New Jersey but work in Philadelphia, PA. My W-2 form shows that NJ State Income tax, NJ SUI and PA SUI were deducted from my payroll this year. I don't believe this is correct. I did have the local income tax withheld. I questioned the bookkeeper and she feels that she is correct.

She is correct. NJ and PA have a reciprocity agreement that allows those who live in one state and work in the other and pay ONLY taxes for the lived-in state.