You may want to consider Vandusen Botanic Garden in Vancouver www.city.vancouver.bc.ca/parks/parks/vandusen/website/

In North Vancouver there is the Park & Tilford Gardens www.parkandtilford.ca/pandtgardens.htm

Hatley Park on the grounds of Royal roads University, on Vancouver Island
www.royalroads.ca/channels/about+rru/campus+information/grounds+and+gardens/default.htm

I'd second the recommendation on Vandusen in Vancouver. In my opinion, Butchart is a "garden where the main focus is on big beds of annuals". It is beautiful, but how many Marigolds and Petunias do you need to see in a lifetime.

In Seattle, I'd recommend the Bellevue Botanic Gardens or Kobota Gardens.

Hearon's wood in Kingston just west of Seattle.
Bloudel Reserve on Bainbridge Island
Fairie Herb Gardens in Olympia if you come south.
All have web pages that can be found in Google.

we come to the nw every july- for the past 12 yrs., and we visit gardens and nurseries.we have been to all the places mentioned so far. Easily the best public garden in seattle is the bellevue botanic garden;it's relatively small but you'll need 2 hrs to do it justice. while you're there in bellevue, go see the terrific borders at wells-medina nursery (10 min from bellevue botan gdns). Heronswood(genuflect, genuflect) in Kingston, is easily one of the best gardens in north america.it is filled with rare beautiful things, and fun exciting combos, and garden art. everything. it requires at least 4 hrs to do it justice and it takes a long time to reach it- ferry,etc., but you could leave seattle early, stop there for the day, stay overnight nearby and head up to canada the next day. you'd not regret it. bloedel is more a property with some lovely vistas and landscapes etc but not designed floral borders, etc.
in vancouver, van dusen is THE public garden to go to. it is enormous as it is located on a former golf course.it is a true botanic garden with all the different parts of the world with their own display areas. it absolutley requires a day to see it all, and there is lovely restnt there. between it and butchart, van dusen is the place you will long to return to.other than van dusen the ubc botanic gardens(also huge) and the ubc japanese garden are the most worthy public garden experiences in vancouver area. unless you are hell-bent on going to butchart( which i have enjoyed for the trees and conifers and vistas but not the floral displays), i think vancouver is better use of your time. if you do go to victoria, the border gardens at Government House are quite romantic and lovely.plse email me after your trip. i'd like to know your experiences.

I didn't bother with Buchart on my trip this spring--not my taste. But I enjoyed the University of British Columbia Botanical Garden

Here is a link that might be useful: UBC Botanical Garden