Is there any National Park that is a day trip from NYC by either car/plane?
I just reviewed my list- this is what I got.
Cuyahoga- fly into CLE
Congaree- fly into CAE
Hot Springs NP- fly into LIT or Memorial Field Airport (no direct flights from NYC, so LIT might be the only option for a day trip)
Gateway Arch (if you consider that a "NP")- fly into STL
Those are small parks so you can cover in a day.
I think Acadia would feel rushed if flying in and out on the same day.
Indiana Dunes might be an option too, but I'd want to hike for more than what would be possible if flying in an out, although you'll probably have great flight options as the closest airport are the ones in Chicago.
Mammoth Cave will be hard to manage if you're flying in and out same day and want to cover 2-3 tours.