Okay, so you are interested in stuff from Nassau County to Montauk. This is the page for you. Long Island is a playground for many people. There are also ways to get from here to Connecticut.
The Friends for Long Island Heritage operates many of the nostalgic places including the Old Bethpage Restoration Village, the Big Duck, Deepwells Farm, and, of course, the Saint James General Store.
If you want more history, just go as far as you can. Namely to the Montauk Point Lighthouse, which has served since 1796.
The island has much to offer, including ferry service to Connecticut. The ferry services take you from Port Jefferson to Bridgeport, and Orient Point to New London.
What about our favorite (debatable point) railroad. Well, it started in the 1830s and is still going well (If you ask some people)
Adventureland is the amusement park where many of us went. It's still giving pleasure to the masses that come to the island.
You can also take a drive to Gurney's Inn and people have been doing so for a long time
Unfortunately all of the drive in movies are now upstate. However, driveinmovie.com has a picture of the Westbury if you scroll down in its New York State sections. There was also the 110 Drive In, the Valley Stream Sunrise, the Patchogue Sunrise, the Bayshore Sunrise (By now I wish the Sunrise Highway wasn't this long for this paragraph would be shorter), the Johnny All Weather, and the Coram Drive In (Now the closed Movies at Coram).
For those people that did not want to brave the elements there were many indoor theaters to their liking including the Lindenhurst, the Levittown, the one at the Smith Haven Mall, the Rialto in Patchogue, the Plaza in Patchogue, and the Suffolk in Riverhead. The Patchogue Theater is now the Patchogue Center for the Performing Arts. If you wish to find any more of your favorites, go to cinematreasures.org