Chris,
Chambers is about 30 minutes from SeaTac. It is a MUST play if you only have one round here. Funny you mention Sahalee - only because if you had to pick the best course most different from Chambers, it would be Sahalee.
Chambers is also the type of course you're goiing to want another crack at, so if you have time for 36, I highly recommend it.
The Home Course is also worth the time if you have it, and it's close to Chambers.
I like Seattle CC a lot more than Sahalee. More diversity in the holes, not everything completely tree lined, no housing, and a lot less play. It is also very different from Chambers.
Both are private though, and would require play with a member. Unfortunately I'll be away during your visit and cannot help out with Seattle but it is a wonderful golf course rarely talked about. They don't allow raters or much outside play as they like to keep it private as possible but I would strongly recommend it if you knew somebody.
Do note I'm generally the minority as far as Sahalee goes. You'd probably like it. I just feel like it is way too tight and the holes can get repetitive.
Aldarra is a lot fun, although a brute, and is also private.
Chambers Bay is really your best bet. It's not only public but the best course in the state.
The Home course had some unique holes but there are several courses I would play before it.
Stay away from Newcastle at all costs. You might as well play the Seattle muni's instead.
My top courses within 40 minutes of Seattle:
1. Chambers Bay (public)
2. Seattle CC (private)
3. Aldarra (private)
4. Gold Mountain - Olympic (actually about an hour; ferry ride out of downtown and five minutes drive)
5. The Home Course (Public)
6. Sahalee (private)
IM me if you have any other questions and I'd be happy to help.
Cheers,
Jordan