Hi CathyM,
I've never stayed at Hotel Plaza Mayor, but I've seen it last trip, a pink colored building is hard to miss. And if it takes you 10 minutes to walk to Puerto del Sol, you'd be walking at a very leisurely pace. The Atocha train station, where you would pick up the AVE, is somewhere between a 20 and 30 minute leisurely stroll.
I just checked the map for the Hotel, and it is right on Calle Atocha, which at the end of, is the Atocha train station. It would be kind of a long walk, not too bad if you're in shape. I'd catch a taxi thought, from the train station to the hotel and vice versa. I guess that's from the point of view of a 45 year old, not on a very tight budget.
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"I swear -by my life and my love of it -that I will never live for the sake of another man, nor ask another man to live for mine."