This is what NY State rules say:
'If you are married and filing separate returns (filing status ?), both of you must take the standard deduction unless both of you itemized deductions on your federal returns and both of you elect to itemize deductions on your New York returns."
I can't quite figure out what this means.
What if spouse files in New Jersey where there is no itemizing or standard deduction, if we both use itemized deduction on federal, would I still be able to take the NY standard deduction?
Yes, you can use the New York standard deduction.
This says that is you're married filing separately that you have to use the New York standard deduction unless you itemized on your federal return and you both agree to itemize your New York return.
In real people language... the default is that you have to use the standard deduction if filing separately. You can decide to itemize but only if you itemized on your federal return and only if both of you agree to itemize on New York.