We went to this area to see the Frida Kahlo Museum, but my son (who lives there) was excited to show us the whole area, for good reason. Coyoacan was once a separate little town, but now Mexico City has engulfed it. Still, you can see the old town gate, that still has bullet holes from some battle in some war. The town still maintains its city square, which is surrounded by a beautiful old church and a number of restaurants. We were there on a Sunday afternoon, so the area was very active with families and people enjoying the weather.
The cafes and restaurants are cheap by US standards, and probably a bit touristy for Mexico standards, but this area maintains its authenticity. It doesn't feel like a tourist trap. It is still an area where many families live. There are schools and markets. It is totally safe. There are street performers and kiosks with all sorts of things for sale everywhere.
The Kahlo Museum is a must see, so if you're in the area anyway, walk around and find a place for lunch or to grab a beer. You'll be happy you did.More