The Cumberland County Historical Society runs several museums in Greenwich N.J.:
The Gibbon House is open Tuesday-Sunday from 1-4 pm but is closed January, Febuary, and March.
The Warren and Reba Lummis Genealogical and Historical Research Library is open Wednesdays 10-4 and Saturdays and Sundays 1-4. It's closed from the middle of December to the 1st week of Jan.
The Alan Ewing Carman Museum of Prehistory in Cumberland County is open Wednesday, Saturday, and Sunday from 12-4 all year.
The John Dubois Maritime Museum is open from 1-4 on Sundays.