Nick, to put it in local terms, if you are moving to LI you will be in NY but you won't be in NY at all. Since Long Island (part of which is in NYC and part of which was once part of NYC, although neither wises to admit this) is "in" NY about the same way that Wheaton is "in" Chicago......
Where you plan to commute to is going to make a difference in where it is practical to keep a boat. Despite our rash of warm winters, it was not unusual for major parts of the local waterways to freeze up in the winter, that's one reason liveaboards are not common here. The few places where you can tend to be tucked into odd corners.
And, did you get your visa yet? Our annual quota on mainlanders coming out for 2008 is already filled, if you don't have a visa they won't let you on the island. [vbg]
Seriously though...NY/LI wx can be brutal, in July and August air conditioning for the combined heat and humidity is not optional. Temps from November to April can range from the 70's down to the sub-teens, you will get a mix of those that has only become more erratic in recent years. Nothing like the nasty lake winds you get in Chicago, but enough to make living on a small sailboat something to really think over.
Marinas here take payments the same way they do pretty much everywhere in the US: Up front, by the month, or the annual or "seasonal" contract for the discount rates. There is no "luxury tax" but you will pay sales and income taxes, and once your boat has been in the navigable waters of NY for 90 days, on the 91st day it had better be locally registered with any applicable taxes paid, or it is subject to arrest. Tax men in the Northeast in general tend to be humourless fellows. Your income tax rates will also be radically different depending on whether you reside in NYC, LI, or other parts of NY.