My favourite from Downtown has to be Stanley Park. Go down to the New Convention Centre where you can see the Olympic Flame and walk west along the new Seawall past Coal Harbour.
This will take you to the Rowing Club and Stanley Park. Follow the Seawall all the way around past Siwash Rock and head back towards the city along English Bay.
Great view of the city and the West side as you come around Ferguson Point after third beach on your way to the aquatic centre. From there grab a water bus across to Granville Island for a keek at the "Granville Island Market" and a java before the last leg around to Vanier Park and Kits Beach.
From Kits you can catch the Number 22 bus back across Burrard Bridge into Downtown.
It's a full day trip but well worth it. About 12 Km from Convention centre to Aquatic Center and another 3 km to Kits beach maybe. And if you are still not happy, you can continue along Jericho and Locarno Beaches all the way to Spanish Banks and the University of British Columbia. The Number 4 will take you back Downtown.
An alternative is to take the Number 250 Horseshoe Bay from Georgia Street Downtown all the way to Lighthouse Park on the North Shore. Ask the driver to tell you when to get off.
The park is smaller than Stanley Park but the views of the City may be more stunning. Walk around the park and head East towards West Vancouver. You can catch the 250 anywhere on Marine Drive and head back into Downtown or change at Park Royal for Lonsdale Quay and catch the Seabus to Downtown.
Map of Stanley Park
http://vancouver.ca/parks/parks/stan..._printable.pdf
Map of Lighthouse Park
http://westvancouver.ca/uploadedFile..._Trail_Map.pdf
More walks and hikes around Vancouver can be found at:
http://www.trails.com/activity.aspx?area=14373
http://www.hellobc.com/en-CA/SightsA.../Vancouver.htm
http://www.bcpassport.com/vancouver-...vancouver.aspx
Enjoy the walks and the city.