Capilano River Regional Park is a free, forested alternative to North Vancouver's paid suspension-bridge attractions, with trails above the river canyon, views of Cleveland Dam, and access toward the salmon hatchery. It is one of the easiest places to feel the North Shore forest without leaving the city edge.
Trails range from short viewpoints to longer wooded loops, and rain is part of the atmosphere. Combine it with nearby Grouse Mountain or Edgemont Village if you want a fuller North Vancouver day.