1.7mi W. Hacienda Station, 925-847-9308,
4682 Chabot Dr, Pleasanton, CA 9458

Well, that is physically closest, but if you check usps.com (where you probably got that from) there are four others within five miles of me. The one you listed isn't actually in the same city as me which may or may not make a difference. Add to that the fact that I can't go to the post office during the week (they close early and I work 45 miles away) and you can see why this is inconvenient at best.

Edit: I called and that post office doesn't handle residential mail (don't ask me what they actually do). The next on the list is not currently answering their phone.

-Mike