We highly recommend a stay with Arturo at his excellent apartment in Central Coyoacan. Right from picking us up at the airport to advice on taxis, restaurants, sights and things to be beware of, Arturo was a ready source of information. He even offered to take us to places which were a little more difficult to visit if one was relying on public transport.
Arturo and his family are in the same block but your apartment is totally independent and you can interact with them as much or as little as you like. The house stands on its own land in central Coyoacan and you are an easy walk to Frida Khalo's house and all the other sights of the area.
Coyoacan itself is a fascinating "village" but accessible to all the sights in Centro. After the pressure of Centro it was a relaxing and pleasant place to eat and walk in the evening.
We had a wonderful time and can't recommend this apartment highly enough.