Kenneth's are all good suggestions, especially Stanley Park if you're pressed for time. You could shoot in the park for an entire day and barely sratch the surface. Near the Georgia Street entrance (Denman and Georgia) you can rent a bike. Perfect for rapid acess to the entire park. Cycling the Stanley Park Seawall is a class ten experience. Do it at off hours, especially very early in the morning or late in the evening. Safe, fun, gorgeous, easy (flat terrain) and a zillion landscape opportunities.
I'll add, on the North Shore
Cleveland Dam, an easy find and a good, short time visit.
Capilano Suspension Bridge, (touristy, easy) or Lynn Valley Suspension Bridge (harder to get to, a hundredth the tourist factor, just as spectacular and FREE
Right next to Cleveland Dam if you have time, the Grouse Mountain Cable Tram is spectacluar. (be on top at sunset) Helicopter rides on top of Grouse are cheap and incredible value since you're already in wilderness. $100 buys you a life-changing experience. Barring the helicopter, the views from the top of the tramway at sunset are quite amazing.
Lighthouse Park at Point Atkinson in West Vancouver for excellent west coast scenery. The biggest trees you'll see in Canada. Rocky Cliffs overlooking the ocean, a lighthouse! A pretty half hour drive from Stanley Park along the shore (Marine Drive) through some pretty tony real estate. Return to downtown via the Upper Levels Highway for a good loop tour and more views.
False Creek, in the heart of the city. Lots of walking paths, good urban landscapes. Restaurants. Bicycle works really well here, too.
Have fun. It's a great city. It might rain.
Peter