Two days is enough to see Montreal’s headline sights and still spend meaningful time in the neighbourhoods that make the city interesting.
Day 1: Old Montreal
Use the morning for Old Montreal and the Old Port. Choose one paid interior rather than trying to enter everything.
Day 1 evening
Stay central if tired, or move to the Plateau for a strong contrast with historic Montreal.
Day 2: Mount Royal
Start with Mount Royal while your legs are fresh, then descend toward the Plateau.
Day 2 afternoon: Plateau + Mile End
Walk commercial streets and residential side streets, eat, and continue into Mile End at neighbourhood speed.