As far as I can find via Google.com, there are no
Mercadona Supermarket's on Gran Vía. The nearest one is near the Moncloa metro station or the other one near Acacias metro station. Does it have to be a Mercadona?
You should find a few dozen cybercafe's/locutorios within 500 meters of your hotel without any problem. 1.50-2 Euros per hour is pretty standard.
Good luck! Saludos, MadridMan
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