Both of these stories are about time, the process of growing old and letting go of things. "El Viejo Tupi" is the name of a cafe, one which the narrator identifies with a particular time and crowd in Montevideo. The cafe is considered something of a local landmark, one of the five places that tourists should see when they are in the city. There's not really much of a plot, mainly that once the cafe has to move due to development, it doesn't end up lasting very long at its new location. From the way Benedetti tells the story, I would guess that he is describing a real cafe, a lost part of the Montevideo of his younger life.
"No hay sombra en el espejo" features as narrator and protagonist one Renato Valenzuela (Is this important? Does he feature elsewhere?) who is looking at himself in the mirror, as he does every day. It is here that he contemplates his life and regrets. Renato recalls his life, his young son, the wife who is no longer with him. It is here where he comes to the conclusion that reflected images have no shadows, no regrets. The image in the mirror may feel no regret, but manages to return accusations. Like Tupi, this story does not have much of a plot. It does make for a moving mood piece, though.