How about going to Fire Island, just for day? Take LIRR to Patchogue, Sayville, or Bayshore, then take ferry over. Beaches are very pretty. But staying there will be expensive in summer. It's about 2 hours total to get there, so you could make it a day trip (just check ferry schedule to coordinate times).
If you want to go to Hamptons, you could take LIRR out there, but hotels are super expensive in summer. Oh even better--take ferry to Sandy Hook, NJ. Quick day trip from lower Manhattan, and pretty. Google Sandy Hook, NJ for ferry info.