Here's a start:

Here is a link that might be useful: Northwest Plant Locator

Here's a cool little nursery that I like in Seattle. It's not really an alpine nursery, but one that specializes in drought tolerant plants, and they have a nice variety. They also sell interesting old items for the garden.

Here is a link that might be useful: Piriformis Nursery

This guy has incredible alpines. I've been to his place, but I don't think he's open to the public, at least not without an appointment. Here's his website, give him a call if you wish.

Here is a link that might be useful: Mt. Tahoma Nursery

I grew up in that area, studied botany there, but haven't lived there in over 20 years. I would recommend (based on memories) visiting the University of Washington arboretum - it has? (had) Japanese gardens. I would also hike in the Hurricane Ridge in the Olympics. Although flowers probably wouldn't be blooming, it provides many great landscape designs! I'd also be tempted to visit Heronswood Nursery - although I don't believe it has alpines, it has lots of exotic species and from what I hear is quite impressive.

Here is a link that might be useful: arboretum

Hearon's wood in Kingswood www.hearonswood.com
Fairie Herb Gardens in Olympia http://daveherbs.home.comcast.net/index.html
There are 2 bonsi collections, one at Wharehouser headquarters called the Pacific Rim Bonsai Collection http://www.weyerhaeuser.com/aboutus/whereweoperate/worldheadquarters/bonsaicollection.asp.

Another is Elandan gardens near Bremerton http://elandangardens.8m.com/

Let me know if you want more information.

A visit to Heronswood shouldn't be missed if you can fit it into your schedule...no matter what type of garden you are interested in, you'll find this garden fascinating.

But you do need to call ahead if not able to be there for a regularly scheduled garden open...worth the effort.

Here is a link that might be useful: visitors info

I'm from Vancouver over the bridge from portland.
Go to www.specialtynursery.org
Tsugawa Nursery has bonsai, they are in Woodland WA, www.tsugawanursery.com
Bonsai Northwest in Seattle www.bonsai_NW.com

Basically, by September most of the display gardens are done for the year.