The vital stats, from the back of the card:
P.O. Box 1 — Dial 693-8176
Oxford, North Carolina
Modern, quiet, comfortable, air-conditioned units — Hot water heat — TV in rooms — Children's playground.
Restaurant & Service Station Adjacent
On U.S. Route 15 — One mile South of Oxford, N.C.
According to a North Carolina history blog: "The John Penn motel built in Oxford, NC in 1954 evoked Mt. Vernon with its white paint and cupola."
You can check out another vintage postcard of the John Penn Motel, with a better view of the building, on this Flickr page.
I found some obituaries indicating that people were still working at the John Penn Motel as late as the mid-1980s, but nothing firm regarding the motel's current status, if it even still stands.
John Penn, by the way, was a signer of the Declaration of Independence from North Carolina.