The town of Oyster Bay comprises about 1/4 of the area of Nassau County and includes a slew of villages and hamlets. This article covers the hamlet of Oyster Bay, which is on the North Shore.
Oyster Bay is the last stop on the Oyster Bay Line of the Long Island Rail Road.
Take Exit 35N from the Northern State Parkway or Exit 40E from the Long Island Expressway (I-495) and then take State Route 106 North.
Oyster Bay is quite an old town, having been established in the 17th century, and it is absolutely chock-full of great old buildings, only a few of which are pictured in this article.
There are also parks, including Theodore Roosevelt Memorial Park. Theodore Roosevelt spent several summers as President in Oyster Bay (now the nearby hamlet of Cove Neck) and died and was buried there. However, if there are signs at parks saying "Residents only," you may be out of luck in that respect.