I loved wandering around Old Montreal. Montreal by itself is a great city for pedestrians and public transportation users. Old Montreal kicks it up a notch with its historic architecture, cobblestone streets, restaurants and their outdoor dining, small boutique shops, souvenir shops, open plazas and statues, etc. Definitely walk down Saint Paul street. You can't miss it, it's the oldest street in Montreal.
I highly recommend checking out Le Robin Square (small family restaurant) and Notre Dame Basilica (closes ~4pm) while in Old Montreal.