Whatever you choose in LI Sound, take your time on the two next legs - for different reasons:
The trip down the East River and out into New York
Harbor will be one of the highlights of the trip. Pick weather to enjoy it. Have the cameras out.
Conversely, between NY and Cape May you have perhaps the most challenging part of the whole trip. The NJ coast can be dangerous and goes down hill fast at this time of year. Wait for perfect weather. It's late - you could wait a week (I won't go if there's any chance of wind above 15 knots in the arc
from NE to SW). If I get a forecast
for a calm -- day or night -- I start the motor
If you get stuck in NY by weather, an expensive but really enjoyable place to wait is Liberty Landing Marina. There's an hourly ferry
that in 15 minutes drops you right in the middle of Manhattan.