You can try the Police Lost & Found centers. Taxi drivers are supposed to return lost items to them:

Bronx
43rd Precinct
900 Fteley Avenue (between Story Avenue and Banyer Place)
(718) 542-0888
Brooklyn
76th Precinct
191 Union Street (between Hicks and Henry Streets)
(718) 834-3211
94th Precinct
100 Meserole Avenue (between Lorimer Street and Manhattan Avenue)
(718) 383-3879
Manhattan
17th Precinct
167 East 51st Street (between Lexington and 3rd Avenues)
(212) 826-3211
Central Park Precinct
86th Street Transverse, Central Park
(212) 570-4820
Queens
107th Precinct
71-01 Parsons Boulevard (between 71st and 72nd Avenues)
(718) 969-5100
115th Precinct
92-15 Northern Boulevard (between 92nd and 93rd Streets)
(718) 533-2002
Staten Island
120th Precinct
78 Richmond Terrace (between Wall Street and Hamilton Avenue)
(718) 876-8500