Does my daughter have to file state taxes with Pennsylvania and New York? Lives in PA and goes to University of Rochester and has work study job earning $14,700?

Yes, your daughter needs to file a New York non-resident tax return.  She must also file a Pennsylvania resident tax return.  As a resident of PA, 100% of her income is subject to PA tax, regardless of where it is earned.  If she pays tax to New York, she will get a credit from Pennsylvania for tax paid to another state.  The credit may not be as much as the New York tax.