[kjell]

Here's a query for the OSM tagged emergency rooms near me: http://overpass-turbo.eu/s/7pL (move the map and press "run" and it will update)

https://www.mapbox.com/blog/coffee-directions/ has a "coffee finder" that will give directions, but replace "coffee" with "emergency room" and it suddenly has a much greater impact.

[maxerickson]

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).