Addition to discussion, in reference to current day place names - referring to Long Island (in New York) is generally ambiguous:
* Geographically, Long Island consists of 4 counties:
- Kings County (which is the borough of Brooklyn in New York City)
- Queens County (the borough of Queens in New York City)
- Nassau County
- Suffolk County
* People who are from that general area, however, think of Long Island as only Nassau and Suffolk counties.
As Ellen mentioned, Long Island City is a community located in Queens, therefore, (to a native like me) it is definitely not in Long Island.
* Technically, by the accepted WikiTree place name hierarchy, Long Island is not any kind of place - it only groups 2 specific counties together (Nassau and Suffolk).