Welcome STV,
Outdoors: Like others have suggested - get a bike. Take in the waterfront anywhere from Coal Harbour to Spanish Banks (Note: walking the seawall around Stanley Park alone takes 90-120 minutes, cycling around 25 minutes - ignore the faster time estimates, they are simply wrong).
To experience a snapshot of nature, explore either Pacific Spirit Park, Stanley Park or, farther afield but accessible by transit, Lynn Creek up to the headwaters (there is even a free untouristic suspension bridge - Capilano's is the definition of a tourist trap).
Neighbourhoods: Move quickly through Gastown to the Down Town East Side, Chinatown (only East of Main), and then either: (1) up to Main Street south of 5th Ave all the way to around 33rd Ave, or (2) ride through Strathcona to Commercial Drive south of Adanac to Broadway. You could also do a loop west along 10th Ave to get to Main.
If you want to see our dying India town its centered around Main and 49th, Viet town is along Kingsway.
Indoor suggestions: Museam of Anthropology, Art Gallery or Aquarium (although I personally oppose their keeping of large marine mammals in captivity).
Other: microbreweries, distillers and dispensaries.
Saddle up, helmet optional, and take in the city! CC
