[Last updated 1/31/22 9:33 AM PT—The Woolworth Diner's last operating day was Sunday, January 30, 2022.]
I have some vague memory of going to a Woolworth's as a child—though perhaps only for shopping, and not for lunching.
Indeed, there was a Woolworth's store and lunch counter on Salina Street in Downtown Syracuse that closed in 1979 (when I was 4 years old)—and the building still stands, having housed a Rite Aid pharmacy on its street level until 2018.
But I feel a certain nostalgia for it regardless. I often feel the loss of things I don't really remember experiencing myself.

circa 2022
So, after having visited the former Woolworth's building and restaurant in Oxnard in 2015, I didn't even think about grabbing lunch anywhere but the extant Woolworth's lunch counter when I was in Bakersfield for just a few hours in 2019.