Montreal was founded by French settlers in 1642 as Fort Ville-Marie, on an island in the St. Lawrence, and the mountain in the middle of it gave the city its name. Today it's the largest French-speaking city in the Americas, with about 1.8 million people in the city and around 4 million in the metro area, and a long-established English-speaking minority. You can read both layers in a single walk: a stone port town from New France, an underground city built for the winters and a concrete stadium left over from the 1976 Olympics.
It's a city you eat and wander through rather than tick off. The sights are good, but the habits are the reason to stay: a bagel from a wood-fired oven, a smoked meat sandwich at a deli counter, a festival in the street in almost any season. Five days lets you do the big museums without hurrying, see the east side of the island that many visitors skip, and spend a full day outside town.
The plan runs by geography. Day one is Old Montreal and the port, day two Mount Royal, the Plateau and Mile End, day three the downtown museums, the underground city and the Quartier des spectacles, day four the Olympic Park, the Space for Life museums and Jean-Talon Market, and day five the southwest and the Expo 67 islands, with Atwater Market, Little Burgundy, Habitat 67 and the Biosphère. The Eastern Townships are in the extras: a four-hour drive for a day that is thin in winter. Start on a Tuesday. The Montreal Museum of Fine Arts, the McCord Stewart Museum and Pointe-à-Callière all close on Mondays in their regular schedules, Notre-Dame Basilica opens only at 12:30pm on Sundays, and a Tuesday start puts every museum on a day it's open. More on the country in our Canada guide. The two big trips from here, Mont-Tremblant and Quebec City, have guides of their own.