Northsore LI
I think the south shore is not great for sailing your size boat,I had a 2001 290 while living on LI and sailed the east end mostly.
I did get to sail over to CT and many nice places to go to as Alan mentioned but if you really want to have a great time go to Greenport and Sag Harbor,great towns to get off the boat and walk around and eat dinner or lunch or Ice Cream and than make the trip to Block Island or over to Mystic for a great places to enjoy.
Before Leaving LI and moving to Florida my wife and I did 4 weeks on the east end of LI and CT.,my wife loved it and she is not a woman that likes to be on a sailboat that long but she had a great time and found all those places very interesting walking and eating in the nice towns in Ct.
Her'sand my most fun places was Mystic,Greenport,Sag Harbor,Block Island,you will always remember it as the best trip.
Nick