Claiming the standard deduction on the Federal Income Tax Return, can one itemize deductions on a NYS Income Tax Return?

Yes.  If it is to your advantage to do this, Turbotax will do it automatically.  You will need to enter all your itemized deductions (including items that were eliminated from Federal tax returns, such as miscellaneous itemized deductions for work expenses) even if you don't expect to benefit at the federal level.