Delta Airlines have round trip airfares travelling to and from Raleigh NC (RDU) and Seattle (SEA) for $167, nonstop. This is a basic economy fare. Delta's basic economy fare does allow one carry-on bag in addition to a small personal item to bring onboard for free.
Or....upgrade to a regular, main cabin economy fare for $30 more.
Depart RDU: Oct 9-10, 16-17, 20, 23, 27; Nov 3, 7
Depart SEA: Oct 2-3, 9-10, 13, 16-17, 23-24, 27, 30; Nov 3, 7, 10, 13-14
Returns: good availability returns, generally for a 7-day stay
Use dates and plug into Skyscanner [skyscanner.com]
then book it with your favorite OTA from the list. For hotels, check Hotwire's Hot Rates [hotwire.com]