There are way too many places to name, so we've included some of our favorite spots to get you started.
Sag Harbor
East Hampton/Amagansett/Napeauge
Southampton / Hampton Bays
We'll level with you, we don't spend much time here, but these are some spots we hear are great
Multiple Locations (check for locations)
Any beach, truly, any beach at all. You can't go wrong.
Most beaches will require a beach pass to park. Gibson and Peter's Pond beaches won't require a pass. You should also ask your hotel if they provide passes or transportation (Southampton Inn provides free transport to/from and Ocean View Terrace Inn has limited passes for guests).
Beaches with parking lots/attendants usually offer parking for $50 on weekdays. Try Atlantic beach, Coopers beach, or Sagg Main beach on Friday.