I've been able to visit two post offices in nunneries. Yes, convents. They're self-contained campuses with non-mobile residents who need the facilities.
The first is in western Pennsylvania, and goes by the name Villa Maria. After taking the circuitous route around the campus, I found the sign for the post office. To visit the post office, I needed to explain the purpose of my visit and sign myself in. Needless to say I was the only 22-year-old New York male in the vicinity!
The post office was closed for lunch when I arrived, and I was able to snap this photo before the Postmaster got back. (Since it's technically not on postal property, it's interesting to see how the post office fits in its setting, and I doubt it puts any security in jeopardy, I'll post the photo here:)
In September '09 I passed through the Bardstown, KY area. The town had two CPUs in banks (one of which has since been discontinued); about a mile north of one of the CPUs was the Nazareth, KY convent. The post office was again concealed on the campus, though this one is in a standalone building: