Where can fluorite be found on Long Island, New York?
I do not know of fluorite being reported to occur on Long Island. If fluorite is found in NYC, the Natural History museum might have specimens.  You might try contacting a mineralogy / mineral collecting club on Long Island. Someone there would probably know for certain if fluorite can be found.

Fluorite can be found in several limestone formations in New York. See map


Personally, I have collected fluorite from the Penfield Quarry near Webster New York during the mid 1980s.  Some of the waste rock from the quarry was used as breaker wall stone on the lake front in Webster New York.  You could probably still collect fluorite crystals there.

Here is a map of the lower 48 states showing mines where fluorite has been reported to occur.  

 

Other places I have personally collected fluorite


Terlingua, Texas fluorspar mine (massive bedded fluorite)
Spearfish Canyon Black Hills South Dakota (fluorite in geodes in limestone)
Closed rock quarry in Pennsylvania near Breezewood, PA


Locations where fluorite is still able to be collected.


Mines/Mountains near Socorro New Mexico
Mt Antero in Colorado, at high elevation.
Bancroft Ontario - fluorite in calcite (fluorspar)
Burin Peninsula, Newfoundland, Canada (fluorspar)


References:

Wikipedia Fluorite

Maps created using  Digital Rockhounds Companion software.