The active-duty services don't track their members by hometown, but a project called the Citizen Soldier Support Program at the University of North Carolina-Chapel Hill does. I can't lift the Oregon map from the site for copyright reasons, but you can click the link and do it yourself.
The data isn't shocking -- there are more vets in the population centers like Portland than there are in, say, Gilliam County -- but it's interesting to see where the heaviest concentrations are. And helpfully, the maps also show where VA facilities are located, which illustrates the challenge of matching veterans' services with veterans.
Unfortunately, I only learned about this program because its defenders are raising the alarm about its closure. Tom Ricks' has a guest post by Kenneth Blackman that describes the problem:"Hey, funding for a program that actually helps wounded warriors is running out!"