Prepare for a longish post - as I do live in one of the top tourist destinations in the world...
The Local Mountains: Cypress, Grouse and Seymour - during the winter you can downhill and crosscountry ski, snowboard, toboggan and snowshoe; during the summer - mountain biking, hiking, and the Grouse Grind.
The Beaches: starting at UBC, you have Wreck Beach (the nude beach) and Tower Beach (no one really goes here, but has a lookout tower left over from WWII, which made sure the Japanese weren't coming to attack); Spanish Banks; Jericho Beach; Kitsilano Beach; Sunset Beach & English Bay. There's always someone on the beach (no matter the time of year) - there's beach volleyball; swimming; skim boarding; wind surfing; ocean kayaking & canoeing; suntanning; rollerblading; etc.
The Sports: If you like hockey, well you're in the right place, we have an NHL team - the Canucks; and a minor league team - WHL - The Giants; we have a CFL team - the BC Lions; a soccer team - The White Caps; a Lacrosse team - the Ravens; and a AAA baseball team - the Canadians.
There are a tonne of restaurants: West Coast, Seafood, Chinese, Japanese, British, Vietmanese, Thai, Malaysian, Indian, Afghan, and so on.
Now the big tourist attractions:
Grouse Mountain Skyride & Grizzly cubs (they are super cute!)
UBC Museum of Anthropology
Vancouver Maritime Museum
Vancouver Art Gallery
Vancouver Museum
Dr. Sun Yat-Sen Classical Chinese Garden
Alexandra Park
Lynn Canyon Park
Queen Elizabeth Park
Stanley Park
Brockton Point at Stanley Park
Second Beach at Stanley Park
Third Beach at Stanley Park
The Lookout at Harbour Centre
Granville Island
Canada Place
Robson Square
Vancouver Public Library
Capilano Suspension Bridge
Gastown Steam Clock
Harbour Cruises
Imax at Canada Place
Omnimax Theatre at Science World
Pacific Space Centre
Science World
Vancouver Aquarium
Bard on the Beach Shakespeare Festival
Canada Day at Canada Place
Celebration of Light
Dragon Boat Festival
du Maurier International Jazz Festival
Vancouver Folk Music Festival
Vancouver International Comedy Festival