LAX Post Office is 24/7 except for Christmas Day. It relocated a bit further from the airport, but it's still very close to LAX. It'd be a bit of a long hike walking though, as closer to a mile away. However, it's right next to Hertz, National, etc, car rentals, so if you didn't have a car you could hop on one of the car rental shuttles & then walk from their facility to it.
My guess is the major metropolitan areas might have a 24/7 at the airport or somewhere in the city.
I know I've used the LAX one plenty of times including the middle of the night.
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Sharon
[This message has been edited by SkiAdcock (edited 04-30-2003).]