Do people often live in Tacoma and commute to Seattle?

We are thinking about relocating, and max could only afford a home in the $600,000 range. We would want decent schools. We are not strangers to 45 minute daily commutes.

So my question is...

-What are some good suburbs? -Do people typically commute from Tacoma to Seattle for work?

Thanks in advance!

Edited to add: Thank you all for your feedback! We are definitely going to revaluate and check out other neighborhoods. We didn't realize the traffic was so horrendous.