I am planning to go from Lake Ontario to Hampton and then to the BVI.
The stretch that I have some questions about is from New York Harbour down to Cape May. I am not sure how long it will take, what the conditions may be, and where to stop, either overnight, or for protection.
I wonder if I can get some advice.
I'm unclear on what your expectations are. Am I correct that the Hampton you mean is Hampton VA? Why are you going through New York Harbor?
If your goal is to get to the BVI then I would launch from somewhere in Rhode Island or Massachusetts to Bermuda (four or five days) and from there straight down 65W to Tortola (although I use clear BVI customs in Great Harbour JVD) in six to nine days.
If you have a particular need to stop in Hampton VA I'd head offshore from Rhode Island or Massachusetts to the mouth of the Chesapeake (three(ish) days). Get a paper copy of the Gulf Stream velocity projections from the Internet before you go and decide based on weather what specific route to take. From Hampton head back offshore southeast until you get to 65W and again head straight for the BVI (eight to twelve days).
If you plan to coastal hop (all the way to the BVI?) and go sightseeing it would help to know where you want to stop and what you want to see.
What boat and what crew experience? What equipment on the boat for communications, particularly of weather information? When are you planning to make the trip?
With respect to NY Harbor to Cape May, Sandy Hook (an hour South of the Verrazano Narrows Bridge) to Atlantic City is 8 to 12 hours depending on weather and boat speed. Atlantic City to Cape Henlopen--which is my preference for staging up the Delaware Bay--is another 7 to 10. I prefer Cape Henlopen to Cape May as it's quicker to get in the current when I'm ready to head up the DE Bay and avoids issues with low bridges and shoaling in the Cape May Canal.
Coming South down the New Jersey Coast, Atlantic City breaks the trip up nicely for less experienced crew. However, if you are planning to go offshore to the BVI then a short hop (such as Rhode Island to Cape Henlopen (less than two days) or straight to Hampton (about three days)) is a good way to ease crew (and you) into going offshore. Even if you are only a few miles offshore and can see the lights, getting people into the practice of watchstanding and continuous sailing is helpful.