Note that I've done none of this, but if you're looking for "closest possible" I'd travel out to the Snoqualmie Pass area and head up something like NF-54 to Stampede Pass. Probably still too much light, but it's an hour one-way. Don't try it in the winter, and a Subaru Outback-ish vehicle would be preferred (though I saw a late-model Mustang come off Stampede Pass this past week). One of these days I'll take my R1200GS motorcycle up there in the middle of the night.

If you're looking for more dark, but more travel time, just about anything between Snoqualmie Pass and Spokane and off I-90 a ways should offer a good bit of darkness. Think US-97 toward the Canadian border: open high desert, not a lot of civilization.