Ashley Nathan --
As I'm sure you know, you'll want to be out of the Caribbean by late May. Many boats come north in late April stopping in Bermuda and then crossing to the East Coast. Another option would be to leave the Caribbean basin somewhat earlier, track downwind to the Bahamas, cruise there for a while and then come north using the Gulf Stream. The entire East Coast is vulnerable to hurricanes between June and November (with the highest frequency between late August and October), but the further north you are in summer the more time you have to prepare (or run and hide) should one come along.
As mentioned above, the Chesapeake Bay is a good cruising ground, as is the coast of New England from Connecuicut to Maine. Maine is best later in the summer (less fog) and is one of the world's best, easily accessible cruising grounds. You could spend the entire summer there and not come close to seeing it all. Both Chesapeake Bay and the NE coast are no more than a few days sail from NYC and you could probably delay your arrival in NYC until late October or even early November to save some money.
I have no personal experience with NYC berthing, but I think you'll find it comes dearly (your strong currency will take away some of the sting). Unless your heart is set on living in the city, there are numerous marinas along the coast of Connecticut where you could lay up afloat for the winter and you'd be less than an hour from NYC by train most anywhere west of New Haven, CT.
As you may know, winters in New England can be very cold with long spells of frigid temperatures -- unlike the UK, in winter the Gulf Stream seems to bring more moisture (often snow) to NE than it does warmth. The Chesapeake Bay area generally has a milder winter climate that may make living aboard more comfortable. You might also consider coming north for the summer and traveling south down the coast for the winter (to say North Carolina or South Carolina), and then return north again in the spring. It would probably take you two or three weeks of casual cruising in the Intercoastal Waterway to make the trip one way. (There are draft and mast height limits in the ICW). Offshore the trip from, say Charlestown, SC to New York would be perhaps a week plus or minus a day or two depending on the weather.
PS -- I plan to be in the Caribbean next winter. Should we share an anchorage, I'd be happy to expand on any of the above....but only if you supply the grog.