I've been working on this over the weekend. Due to imported data, the quality of hospitals in OSM (for the US) is pretty low. There are hundreds of doctors offices, clinics and nursing homes that are listed as hospitals.
(I've been correcting the data in my region. I have the idea to do some analysis for the entire country and incite people to clean up their areas. The Medicare dataset mentioned in this thread really makes that easier.)
That query works better than just looking for hospitals.
At a glance the rest look okay, but I converted one of the results into a 24 hour clinic (which is a better semantic match for urgent care than hospital+emergency=yes).
(I've been correcting the data in my region. I have the idea to do some analysis for the entire country and incite people to clean up their areas. The Medicare dataset mentioned in this thread really makes that easier.)