The North Fork of Long Island is a beautiful summer vacation spot - although there are far fewer hotels than you'd expect. Most places require reservations and a two-night minimum, and some will be expensive. There are plenty of B&B's or AirBNBs around, but very few traditional hotels. Anyplace in Greenport or Southold will be convenient for you to get to any family events. Surrounding towns are fine as well, traffic is not an issue (except in downtown Greenport on weekends).
My favorite spot - it's inexpensive and dated (think 1950's kitsch, and not in an ironic way), but clean and beachside: The Silver Sands Tell them Shane Curcuru sent you (they might still remember me, we used to stay there every year).
Beyond that, try your favorite travel site. You'll need to look in unusual spots; there aren't any chain hotels.
We have several places where family is staying that might have a free bed.
Pat & Ed's beach house at Paradise Point will be clean - and Sherry Griffin and her boys will be staying there. Front bedroom (single), Side BR (single), Back BRs (two rooms) two twin beds each. Also, people could bring air mattresses if they like there. Let Shane know if you'd like to stay there so we can organize it - there may be more room on the couch or on an air mattress (if you can bring one).
Pat's home aide helper will have cleaned Paradise Point and refreshed the sheets, but be sure to bring your own toiletries and what-not.
Shane's rented cottage in Greenport: I'm staying in a rustic cottage on the beach, and will probably have one free bedroom with a double bed. If you like your coffee strong, and don't mind helping with the cooking & cleanup, let me know if you want to stay with my wife and daughter and I.
Georgia, Barne, and Nan will be staying in a cottage next door to Shane in Greenport (they're full up).
Howell Home will have Kevin's family staying there, although you might be able to bring an air mattress (Check with Kevin or Julie Curcuru directly).