Depending on definitions, driving distance would include Cape Cod and the southern coast of Maine, such as Kennebunkport (spelling?). To the south, the border would probably be around northern North Carolina, but of course a lot depends on your starting point in New York. I think some of the more isolated beaches near the Chesapeake would be nice. IIRC there are some chain aspirational properties in this area, but I don't know which are right on the beach.

For Long Island, it's mostly independent beach hotels and to me they don't seem at all nice for the prices, but there are probably exceptions. If you enjoy wine, doing some of the eastern (generally south fork) Long Island wineries would be fun. You could also do an excursion with the ferry to Shelter Island. For romance, there are some nice inns and elegant B&B places, but they tend to be in villages rather than on the beach.