Adding a few things that have not yet been mentioned:
*San Angel neighborhood (art market and cute shops on the plaza) and lunch or dinner at the San Angel Inn (gorgeous converted hacienda with great food; a Mexico City institution).
*Museo Dolores Olmedo - converted hacienda with peacocks walking all around on the lawns (they frequently have art festivals; music; dancing, etc.). The museo is relatively close to Xochimilco (the canal/boat area) so I would do that in the morning then go to Museo and wander around the grounds/get lunch there after.
*Coyoacan neighborhood/plaza/church - lovely lovely neighborhood with cute restaurants on the plaza - walking distance from Frida Kahlo museum. Be sure to book tickets for the museum in advance they sell out weeks ahead of time.
*I have stayed at and like the Best Western Hotel Majestic on the Zocalo with incredible views of the cathedral/plaza (from some rooms and from a lovely dining terrace). Not fancy but clean and comfortable (old world wooden furniture), and the location is fantastic. You are right in the middle of the historic district (also known as the "plaza de las tres culturas").
*On another visit, I wanted to stay in Coyoacan, and we enjoyed our stay here:
https://casamoctezuma.com/en/
The city is massive and traffic is horrific, so you really want to plan your days by area. Uber is easy and safe, or hire drivers/tour guides.
Have a great time!