Go for a walk up the mountain! For anyone coming from an actual mountainous region, please note it is more of a hill than a mountain. It does however provide for lovely views of downtown and a chance to be in nature in the middle of the city!
Old Montreal is beautiful and distinct. As the historic neighbourhood of the city, it's lined with buildings that date as far back as the 17th century. If you're looking for a museum, the Pointe-a-Calliere explores the history of the island. Rue Saint Paul is one of the main thoroughfares, with shops, galleries, and cobbled streets, it's charming and historic!