24 hour Post Office Lobbys...

I think that could count as Tresspassing on Federal Property, which happens to be a felony. I'll stick to simple Tresspass which is a misdemeanor or even an infraction in some places. I don't fuck around a Fed property.

I stayed in one in Drumheller, Alberta, Canada. It was kinda awkward but did the job of keeping us warm. Only had a person come in once, then around 5:30am two women employees came in. Near opening time they told us we had to leave but they were pretty nice about it. I know it's maybe not the best place to sleep if you're trying to avoid the cops, but it worked out for us. in Canada. No experience in the States but I can imagine it'd be more difficult...

Its hit or miss...those that are near the applacian trail get hikers all the time waiting to uload or pick up care pacages

Yeah, it might be federal property, but the question is, would a federal attorney really want to waste their time prosecuting some bums caught sleeping in a PO? I wouldn't really be all that worried.
My larger concern would be people coming in in the middle of the night, it sounds worth a try though.
I have a buddy who slept in a bank ATM lobby and made it to 6am without anybody coming in.