Actually, you can spend in the $40-$50 range in Seattle and do very well when it comes to golf. It's not like Phoenix or Vegas where multiple courses get into the $100+ range.
So, some suggestions. Are you travelling by yourself, or with a 4-some? Either way, here are some thoughts:
Gold Mountain - This is a 36-hole complex in Bremerton. From Seattle, you can take the ferry to get there. I think it's about an hour each way, maybe more, but you're not really driving much of it. Kind of fun to take the ferry too.
As you can see from the web site, the Olympic course is hosting the 2006 USGA Public Links championship. I think it's a fantastic course - don't let the price fool you. No houses on the course, lots of trees, and some really tough holes. Probably my top recommendation.
Washington National - Even though I'm biased against this one, being a Coug, it's still considered one of the top courses in the area. It is a bit more expensive than Gold Mountain. Probably a 30 min drive from the city.
Druids Glen - Good course, tough layout. Lots of trees, and some tough water par 3s IIRC. Also about 30 min or so from the city, maybe a touch more. They have a new clubhouse and brewpub there, which is supposed to be decent, I haven't been there in a while.
Willows Run - Another 36 hole complex. Very popular, they have some good deals there to play 36 sometimes, although I don't know about Fri-Sat. More of a links-style setup.
Those are a few recommendations. If you want to drive north about 45 min or so, Kayak Point is another good one to check out. Oh, and Trophy Lake is supposed to be great as well - that's probably a solid hour at least though from the city.