There were actually four Hector’s cafeterias in Times Square, according to a 1970 New York Times article chronicling the closing of the last one on 44th Street and Broadway.
I don’t know which one is in this 1952 photo—nor is it clear which Hector’s was chronicled in the opening pages of Jack Kerouac’s On the Road:
“Dean had arrived the night before, the first time in New York, with his beautiful little sharp chick Marylou; they got off the Greyhound bus at 50th Street and cut around the corner looking for a place to eat and went right to Hector’s, and since then Hector’s Cafeteria has always been a big symbol of New York for Dean.
“They spent money on beautiful big glazed cakes and creampuffs.”
Desserts seemed to be Hector’s specialty. “The dessert counter, 12 feet long and three feet high, was a gourmond’s dream,” the Times article says.