I was in Oaxaca last year and my wife has spent a lot of time in Oaxaca City doing church work. I believe not many expats live in Oaxaca City. I believe most travel to the beach towns from there. Living at the beach makes getting to shopping and medical an issue. The mountain road between the two is an issue for most and don't think the new road will ever get finished. We love those beaches but not the roads getting to needed services. We just bought in Sonora state on the Sea of Cortez and love it here. It being in the 'free zone' is a real plus for moving and living.
There is a good size expat community in Oaxaca City and the surrounding villages. A few thousand year round and much more during season. I have lived there for 8 months in El Centro. The expats are spread throughout the city and not concentrated on a specific area. Oaxaca is very safe with little violent crime and what there is is usually politically motivated in some way. Like any good size city, there are areas to avoid at night. But Centro is well lit, good Police presence and very safe.