Best route to Boulder Co. from Tacoma Wa.

Carrying chains is always advisable in the mountain west. Dont want to chain up, dont go. There will be places and times that you either have to sit it out or chain up. As for travel? North out of Denver to I80 west to I84 west. Just west of Pendelton,OR 395 North connecting to I82 and I90 into Seattle, and I5 south to Tacoma. As an alternative, I84 clear into Portland and I5 north to Tacoma.
There are several places weather will cause you problems. Thru Wy, Id, and eastern Oregon are all potiential bad areas.