Central Touring Location in Madrid?

The area near the Prado, but closer to the Reina Sofía might work. The other main attractions in that area are Retiro Park, Alcalá gate, Fuente de Neptuno, and Plaza de Cibeles. That area is close to a metro stop and Atocha train station (day trips to Toledo or Segovia). Depending on where you want to go, you may have to go to one of several other stations. The historic center (Plaza Mayor, Puerta Del Sol) is about a 20 minute walk from there and an additional 10 minutes to the Royal Palace. We’ve been to Madrid numerous times and the last couple times stayed at Hotel Europa at the Puerta Del Sol.

On a 2016 trip when I expected to (and did) spend a substantial part of my Madrid time in the three major art museums, I stayed very near the Reina Sofia. I found it convenient for my purposes. A plus was that this strategy put me near the botanical garden, where I spent some arrival-day time outdoors. Proximity to Atocha Station will be convenient for some potential day trips, as already mentioned.

Perfect! Thank you both very much. I booked a hotel near the Thyssen and Prado.
I appreciate your help.
Lee

Ten years ago we took Rick Steves' travel guide recommendation and stayed at the Hotel Europa overlooking the Puerta del Sol and had an enjoyable experience. That area is centrally located.