The most obvious place to look for cemetery information is on the death certificate. If the person was cremated the DC *should* note this as well.
Death certificates are not online but indexes of NYC vital records are. This site:
www.stevenmorse.org has the best search engine to access the info. If you can locate the DC, you can request a copy from the NYC Municipal Archives online at
www.nyc.gov/records.
Brooklyn's Greenwood Cemetery has it's interment records online (
www.green-wood.com). It's a huge cemetery - you might want to take a peek, just in case you get lucky. Other than Trinity, there are no (large) cemeteries on the island of Manhattan. There are, however, a number of really big ones in Brooklyn and Queens.
Good Luck!
Lynn