Are there any Dutch elements left in New York City or State?

Answer 1

Yes! I went on a walking tour of Harlem, which actually was where the original Dutch settlements were. There are many streets of Dutch styled buildings which are very impressive and well worth a visit. Get on a walking tour if you are there.

Answer 2

There are no remaining original Colonial Dutch buildings in Manhattan beyond some long buried, hidden foundations. The outer Boroughs do have a few surviving farm houses. Upstate New York has a fair scattering of Colonial era Dutch buildings, mostly if not all of them are farm style houses. Perhaps there are a few original Colonial era Dutch Reformed Church buildings upstate but I'm not even sure about that. Most existing Churches are of later construction.
Dutch Colonial Revival Architecture dating from the 19th century can be found in New York City, throughout the state & the nation.
There are words in our language that have a Dutch Colonial origin (see sources) but I assume you're only asking about architecture.

Answer 3

Many townhouses in NYC are built with high staircases (stoops) that lead to the front door. This is a typical feature of the Dutch architecture. In Netherlands, floods are a frequent danger, so the Dutch built their houses with high staircases.

Answer 4

They still refer to the pavement (sidewalk) as the 'stoop', which is a Dutch word 'stoep' and still used in the Netherlands.