Hello,
I’m headed north via Madrid. I arrive in Madrid Chamartin at around 9am and need to be at Madrid Puerta Atocha at 1pm. I have been to Madrid a couple of times but not for years. Any suggestions? Preferably using public trans?
The charming El Retiro Park is right next to Atocha, I would probably spend some time there to relax, stretch your feet before the next train ride. Using public transport it takes about 30 min to get to from Chamartín.
The Botanical Garden (modest entry fee) is also near Atocha. If you're into art you could check your luggage at Atocha and make a quick visit to the Reina Sofia, Prado or Thyssen. However, I don't know how much time you'd spend checking and later retrieving your luggage.
As acraven mentions, but to emphasize what was previously said, I would point out that the 3 art museums mentioned above are close to the Atocha station. The Prado is, some say, either the best European art museum in the world or at least in the top five. But it's crowded and you would want to reserve it in advance so that you don't spend an hour in line.
If you've been to the Prado, etc. already but haven't been to Madrid in several years,
then consider checking out the Caixa Forum next to the botanical gardens, just slightly closer to the Atocha station.
Right now they have an exhibit of Alexander the Great's souvenirs from his own travels in the Near East (or as they say in Madrid, the Oriente Proximo)
https://caixaforum.es/es/madrid/p/lujo-de-los-asirios-a-alejandro-magno_a9279631
Good cafe on the top floor, too.