I live in a pretty gorgeous place, the Rockies are an amazing backyard. It's easy to take for granted all of the amazing hike, views and lakes that we have right here. That said, if i could choose/afford to live in one place in the world - I think I would choose North Vancouver. We have family that lives at the base of Grouse Mountain, and ever since I can remember it's been tops on my list. Who could say no to having mountain biking, canyon walks, hiking etc only steps from your front door. It makes my mountain playground look really far away!
There are many lovely hikes in the area, however my fave is the Hannes Valley trail. It's not an easy hike - 16KM one way, through boulder fields, past waterfalls and some small rope climbs. You start at the base of the mountain, crossing easy bridges like the one above - and end up at the top of Grouse Mountain (don't forget to bring $10 to ride the tram down).
You can learn more about the hike here:
https://www.vancouvertrails.com/trails/hanes-valley-trail/
Make sure you come prepared, lots of water and food - and as suggested in the site above, it is a back country hike so register on the signup board so that people know you're back there.
In the same general area there are much easier hikes and walks, specifically Lynn Canyon. Not only is it a great place for walking it's a great place to hang out when it's warm. There are walking and running trails, as well as a deep enough pool that brave people go cliff diving.
And of course there's the wonderful suspension bridge. Most people only go to the Capilano suspension bridge, which is bigger....but much busier and it's pricy. This one costs nothing and between you and me...the photo opportunities are better. Especially if you're not made of sugar...and brave a bit of rain.
Of course once you're done all this hiking - I'd recommend going back to Vancouver proper for some Ramen. I'd bet @crimsonclad would have some good recommendations :)