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The diner inside is not as seen in the show, but the sign is still there and there's local history behind it. There are framed newspaper clippings and the menu acknowledges the show's three waitresses: Alice, Vera, Flo and the owner: Mel.
I'm surprised you were the only one that pointed out Tarantino. I just rewatched Pulp Fiction today. The long uncut scene where Vincent Vega (John Travolta) and Mia Wallace (Uma Thurman) enter the 1950s-themed diner is absolutely masterful.