Your boat is not USCG registered
, registration is a state motor vehicle process. The fact that it may be USCG documented
will not affect your need to pay state registration fees and use tax.
You need to contact two New York state departments to get answers. The Dept. of Taxation and Finance, 1-800-225-5829; fax 1-800-748-3676
who will now be in charge of collecting taxes including use tax from you, if any is due.
And the NYS DMV, who are in charge of registering your boat and collected associated fees, included any use taxes that may be due in lieu of sales tax. Depending on when you bought the boat and how long you have owned it--you may have to pay the difference between the Chicago sales tax rate, and the local rate in New York. (That varies by city and county, expect a little under 9% in the LI area.) They'll tell the specific time periods. 1-800-call-dmv or www.nydmv.state.ny.us/
where the answers may be online, someplace.
There are no marinas in Garden City. With a car, your only practical commute may be Capri or someplace else in Port Washington, unless you find someplace on the south shore (north shore of the Great South Bay, south shore of Long Island) where the water can be quite thin. Without a car...there's no good way to get into Garden City. Heading the other way, you might find something in Oyster Bay, north and east of where you will be.
And, you'll pay $75 for a 3-year state registration. The good news is that both the DMV and the tax people often do a very good job on the phones (or by email) and they can probably get you the right answers within the hour.