This time of year, the best place to be is outdoors (assuming it is not pouring rain) You may get on and off rain, but don't let that dampen your activities

Places to walk around and browse in stores:
Granville Island Market (close to downtown)
Gastown (downtown) - not a favorite, more of a tourist trap IMO
Lonsdale Quays (not downtown) - fresh seafood

Places to shop in earnest
Robson Street - downtown
Denman Street - downtown
Granville Street - between 4th and 16th

Places to drink coffee, hang out and people watch
Kits Beach
Clark Street
English Bay

Nude beaches:
Wreck beach (near UBC, you will definitely need detailed directions!)

Places to run/walk/rollerblade/mild hike:
Stanley Park
Seymour Demonstration Forest
Pacific Spirit Forest (no rollerblading)
Grouse Mountain (grouse grind hike is only for very fit people)

Stanley Park:
Deserves its own category. 1,000 acres (larger than Central Park) of trails, lagoons, botanical gardens, 7 miles of paved seawall, mini golf, tennis courts, monuments, totem poles, and home of the Vancouver Aquarium. Located right downtown.

A downtown restaurant to note, the Macaroni Grill. Low-mid price range, decent pasta, not fancy. It is an old mansion that has been redone into a restaurant, it's a pretty cool place.

If you are looking for events that are going on when you get there pick up a Georgia Strait. It's a free entertainment newspaper that has most everything you might want to do in there, including restaurant reviews etc.