Sid, Mill Creek isn't really Seattle area!!! (30 mi) . But the G/R is not a zipper... it's just far away,, well publicized, and oh, the fly guys love it......
Anyways, I used to hunt birds and camp at Central Ferry and then drive to the G/R to fish. If you drove straight thru, I'm guessing 7-8 hrs. After you get to Asotin you've got about another hour or so over the pass to the river.. Don't go to the lower river,, monopolized by 'fly fishers'.. Call Kaufmans or another fly shop about driving time.. If you have never been there, GO, it is beautiful in the Fall and no heavy pressure. 3 days or more best.. Listen to chukars cackle on the hills, maybe see some Bighorns, snakes should be dormant.