Robin, The Vancouver crew will chime in for that area. I'm not current in what is big over there, so will start with a few from this side of the pond.
Victoria:
Royal BC Museum
Fort Rodd Hill NHP
Ashton Armoury Museum
Canadian Scottish Museum at Bay Street Armoury
Buchart Gardens
Craigdarroch Castle
Hatley Park ( ex Royal Roads Military College, now RR University)
Drive up Mt Tolmie for a view of the city
Air museum at Pat Bay Airport (check for correct name)
Up Island in no particular order of location:
Comox Air Force Museum
Cathedral Grove Provincial Park (big trees right at highway)
Martin Mars water bomber at Sproat Lake, Port Alberni (Coulsons)
Francis Barkley freight boat day trip from Port Alberni to Bamfield return. -real west coast boating out the fiord like Alberni Inlet
Tofino / Ucuelet on the Pacific. Lots of things out there.
Tired yet? I'll add more as I remember. Most can be researched on line.
Have fun,
Jes