From Pioneer Square tram to Seattle airport, fly to St. Louis airport, then train to St. Louis. 6hrs 55min $214. From Seattle, WA train to Chicago, IL then train to St. Louis, MO. 2days 02hrs $415. From Seattle, WA bus to Portland, OR, line 1337 bus to Salt Lake City, UT, line 1318 bus to Denver, CO, then bus to St Louis, MO. 2days 04hrs $425.