The train from Atocha in Madrid arrives about 25 minutes from its departure. As you exit the train station, go to the sidewalk on the street and catch the city bus up to Plaza Zodocover. From there you can easily get to the places you mention on your own. Walking is easy, but as you know, it is often up and down the hill! You can get city maps at the train station and check on line before to get the general location. When you get ready to return to the train station, take a taxi ride for the ride of your life! Entrance to the cathederal is now on the side, not the same entrance you would have used on a prior trip. There is a ticket office and shop there, it is well marked. I have not found a tour group to join on my visits there, but have searched out the places on my own.
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Silver Traveler