Sephe's suggestion of doing a Suitability Analysis is probably the best way to go.
Another idea - If the primary access to these Emergency Health Services locations will be by driving, one potential analysis you could do would be to use the Network Analyst Extension to determine how accessible services would be by road. You could do a Location-Allocation analysis.
Network Analyst - Location/Allocation - See "Example 1: Locating an ERS center"
ArcGIS Help (10.2, 10.2.1, and 10.2.2)
Network Analyst
ArcGIS Help (10.2, 10.2.1, and 10.2.2)
Network Analyst Tutorial
ArcGIS Help (10.2, 10.2.1, and 10.2.2)
Caveats/Considerations: You will need to have a copy of Network Analyst. Second you will need a good road layer that is set up for Network Analysis. While road layers are fairly easily acquired, getting one that is clean and easily converted into a Network Dataset so it can be run in Network Analyst can be more problematic. It can be a nightmare to try to clean up a road network - many road layers look great visually but have very small disconnects that cause the Network analysis to go awry. Lastly, learning Network Analyst can take some time, as it is a bit different than other aspects of GIS, so take that into consideration if you haven't used it before. Don't get me wrong - Network Analyst can be very powerful; but the level of effort required to get to the analysis stage can often easily be underestimated.
Chris Donohue, GISP