Three Days is About Right
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The most direct route between Tacoma and Boulder is a little over 1,300 miles so you can cover it very comfortably and safely in three days with time for a few modest stops along the way. The route is as follows: I-5/WA-18 to I-90 east, then at Ellensburg switch over to I-84 (south)east. Follow that (It will be duplexed with I-15 in Utah, but stay with I-84 when they split again at Ogden) to Laramie WY and use US-287 as a cut-off down to I-25 south. Finally, CO-119 will take you through Longmont to Boulder. Two roughly equally spaced towns along that route for overnights would be Ontario OR and Evanston WY.
AZBuck