The Dutch Diner, a 1950s Silk City, was located at 501 East Main Street, Palmyra, PA. It had an extensive dining room addition out the back, and a large arrow diner sign.
Looking at GoogleMaps (what a great tool), there may still be something there. The diner sign is instantly recognizable, though now it reads “Pet HQ”. The dining room additions are also recognizable from the post card.
The diner portion itself it a bit more questionable. What’s there is of the right dimensions, and has a vestibule in the same location of the same size and shape, but the entire place has been roofed and sided over. If the diner is still inside, which it wouldn’t surprise me in the slightest if that’s the case, I’d bet you dollars to donuts that there’s nothing but the shell, and that it’s probably all but unrecognizable at that.
On to the second possibility for today, the Wallingford Diner of 47-1/2 North Colony Street, Wallingford, CT. Again, the building that’s there is in the right place, with the right shape, right proportions, door in the middle, door on the end. False deco-facade on the end that’s clearly not part of the building proper. It was opened by at least 1929.
The Wallingford diner was sold in May 1937 ( story 02), in 1962, by which point the streets had been re-numbered and the address was 45 N. Colony St.
Then again, it could be an entirely unrelated bar, but with all the re-numbering, and possibly the move of the diner from parallel to perpendicular with the road, it’s hard to say for sure.
Diner Hunter 
This comment might not help solve your mystery, but I just wanted to point out that the building pictured here as the “Nail 2000” establishment was the subject of a John Baeder painting in 1974. Page 67 of Baeder’s original “Diners” book (Harry N. Abrams, 1978) features a painting of the front of this building when it was a restaurant called the “American Grille.”