Mystic is about 80 mins driving from most parts in NYC.
COney island is the onyl acquarium that I know of worth mentioning. There is one out in Riverhead which is th elast exit on the LIE. 70 min drive no traffice from Brooklyn/Queens.
The Coney island acquarium is quite pitaful, some nice large fish but nothing fabulous. Only good thing about Coney island is going to Nathans and grabbing a few dogs.