To determine the correct fee you have to use both the registration fee and county use tax charts.
What fees apply if my vehicle is registered in Manhattan, New York.
For the renewal or original registration of all passenger vehicles, the vehicle use tax is 80$ for 2 years and for livery and for-hire vehicles in these registration classes, the fee is 400$ for 1 year.
Okay, that's it. Now, let's talk about renewal. Would I get this money back as soon as I return my plates?
When you surrender your plates, your Receipt FS-6 T indicates if you are eligible to receive a refund.  If you are eligible and you do not request a transfer receipt, the refund will be processed automatically and you will receive it in the mail in several weeks.
What was the form that would indicate if I am eligible for the refund?
Your Receipt FS-6 T indicates if you are eligible to receive a refund.
How do I apply for a full 2-year refund if my registration was never used?
You can apply for a refund of the 2-year registration fee only if the registration was truly never used and it is not more than 60 days from the date the registration was issued.  A processing fee of a dollar is subtracted from the refund amount.  To apply, you must surrender the vehicle plates and the unused registration sticker and stub at the DMV office and request a 2-year refund.  If you are eligible, the DMV will issue a receipt that displays two year refund.
What procedure to I have to follow to get this refund, though, if I have changed my name?
You must still surrender the vehicle plates at a DMV office, but request a transfer receipt, not a refund receipt.  You will then send that to the address of the Request for Refund MV-215 form along with the completed and signed Request for Refund [1] MV-215 and proof of the name change such as a marriage certificate, divorce certificate, or other court papers.   At that point, the DMV will issue your refund in your new name if you are eligible.
Will the DMV issue a refund if the registrant died?