Quirky little museum with a permanent exhibit on the settlement of the city of Montréal plus two floors of changing exhibitions -- currently (Feb 2015) an exhibit showcasing Montreal artists of Haitian origin (their art plus their personal connections to the 2012 earthquake) for Black history month, and a clever exhibit about gambling, speakeasies, brothels and corruption in Montreal from the 1920s to the 1950s (plus ça change...). All of the exhibits were extremely well thought-out and interestingly presented.
Plan on spending about an hour here (more if you really want to watch all the videos). Other good options in the area are the Centre des Sciences and the Musée Pointe-à-Callière.