I can't help you with accomodation, but in my 5 trips to Mexico City, I have only scratched the surface.

To get to the Teotihuacan Pyramids by public transit this link provides the routing I took my first time.

https://thewholeworldornothing.com/how-to-get-to-teotihuacan/

Make sure you take some bottled water.

The Frieda Kahlo house/museum is best done via a tour bus. The number of people allowed inside is controlled. Regular and online scheduled entrants can wait 2-3 hours to get in. Tour buses are escorted in directly.

The tour bus I took was part of 10-15 parked at the side of the Catedral Metropolitana de la Ciudad de México on the Zocala. It was about a 5 hour tour (I recall) and stopped at the Aztec Stadium (football), Xochimilco (canals and boat trip), Frieda Kahlo museum, and an upscale artisian store.

I recommend it.