Came here a few times. It's located right in the middle of Old Port near the river. The beavertail is definitely a special treat (local flavor). The first time I heard the name I was quite silly and thought the delicacy is really a beaver's tail. But it's actually fried dough in shape of a beavertail topped with other yumminess of your choosing. (e.g. Cinnamon Apple, Chocolate Nutella, Hazelnut) We got Banana & Nutella chocolate Beavertail, the dough was warm and soft, with melted chocolate. Deliciously sinful experience. The second time was very crowded, since it's right after the fireworks festival (be prepared to sweat waiting for the order). After purchasing the tail, there are plenty of places to sit next to the river and enjoy. The place also sells ice cream as well as smoothies.
I would recommend sharing one with your loved ones - tasty it may be, it is a very heavy type of sweet treat.