I grew up in Olympia, and it's a great place. I would forget about Tacoma, for all the reasons previously stated.
It has a small townish kinda feel, and a fair amount of activities to do. Plus, less than an hour from Seattle. If you like outdoors stuff, its a great place.
Your stats are fairly correct, except for the snow. Olympia really doesnt get that much, and when it does snow its usually less than a few inches. One thing I can say, although it is overcast alot, when its clear and sunny, there is no prettier place in the country (and I've lived alot of places).
Economy is about as stable as Phoenix, although WA in general is fairly heavily taxed. Politically it is very liberal. Very. Oh, no state income tax also.
The largest industries are Microsoft and all of it's subsideraries, Boeing, and Weyerhauser. Very politically correct, and lots of environmentalists.
Truth be told I am contemplating moving back; however, I am very conservative politically, and despise alot of the actions of environmentalists. You really cant avoid em.
Cost of living is OK, about average. I would say housing included probably 10-15% less than Phoenix (I've lived in Phx also hehe).
The music scene is simply amazing, and one of the things I miss most. Whether its jazz, classical, metal, whatever, you will find it there. Along with music, the arts are very prevalant also.
Did I miss anything?