A museum of Canadian history in downtown Montreal. It has an interesting mix stretching back to the First Nations and forward to modern Canadian culture (including a table hockey game), with interesting exhibits on immigration and the language divisions in Montreal. It's not a massive museum, the sort of thing you could pack in on a lazy morning before lunch or over a couple of hours in the afternoon.
Its closest competition is the Pointe-à-Callière museum in the Old Port. The McCord doesn't have the same impressive building or setting as the latter, but it's cosier and the collections are just as interesting. I think the distinction is that Pointe-à-Callière focuses on the history of the region, whereas McCord's remit includes the whole of Canada.
Free admission on Wednesday evenings!