Definitely, my coffee shop would be a coffee shop-library-with the right to bring pets.

There you could sit for hours and let your coffee get cold while you've been enraptured by a novel. It would be a coffee shop with tables under trees, and, why not, since we're talking about dream coffee shops, I'd love it to have little tree houses, hanging shelters where you could retreat to with your coffee, your book, and your cat. Listening to the birds (and making sure the cat doesn't eat the birds).
It would be a cafe with live music on Saturdays (I don't know why on Saturdays): a little jazz or some soloist, in short sets spaced throughout the day.
I would like it to offer an extensive menu of coffees and teas, with espresso, or any of the chocolate presentations, and I would also like the carajillo. I wish it also offered those fruity coffees, which I read about in a post by @macchiata.
Glass cups to be able to appreciate the color of the drink and all the luminous and chromatic game that comes together in a drink like coffee or tea (which can have beautiful colors and transparencies where one can get lost)....
Finally, I will show you the exact location of my coffee shop, so that you can see what the place looks like both during the day and at night.

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As you can see, the only thing missing is the coffee shop I dream of and uistedes to keep me company.