The area around Eagle Lake (Bluffs) has some great dog-friendly hiking trails, and spectacular views of looking over the ocean, Vancouver and Bowen Island.
Dogs are not allowed in Eagle Lake itself, but the trails in the surrounding area are off-leash (see the map below). There are a number of trailheads providing access to this area, including the Whyte Lake trail.
When hiking with your dog around Eagle Lake be sure to keep your dog on the trails and out of the lake.