The Lynn Canyon suspension bridge is a great free alternative from the tourist trap Capilano suspension bridge charges upwards to $40 just to get in the park. Both suspension bridges are located in North Vancouver so the sights and scenery are almost similar but Lynn Canyon doesn't have a tacky souvenir shop and not a lot of people.
It's a great hike to the bridge and beyond. Past the suspension bridge, you will come across a 30-ft natural pool and a waterfall. It is also an entry point to the Baden Powell Trail which is an extensive trail that connects all the parks in the North Shore mountains. You can also make a detour to the Rice lake and maybe go fishing there.
Pay attention to when the park closes since they close the gate to the parking lot. You won't be able to pick up your car until it opens the next day!