You haven't said anything about *what* kind of company you want to work for? Established? Startup? Tech? Non-Tech?
There are half a dozen fortune 500 companies that are *not* regular old tech companies that are either head quartered or have major operations within 20 miles of downtown Seattle. Many of these companies have huge IT departments running their ecommerce sites or internal systems (think Nordstrom's, Costco, Starbucks, Expeditors, PACCAR, Boeing). And that doesn't count a dozen or so other major regional companies such as the local hospital systems and insurers. Many of these companies have a multitude of openings and often times opportunities for quick advancement because Amazon and several other local companies have hired away many of their employees over the last 2 - 3 years by throwing gobs of money at them.
Also as several people have noted the unemployment rate in Seattle is low but not so low that people will pay for your relocations, unless your skills are phenomenal.