Here is an example of what I am looking to do:
Which town in South Dakota is farthest from a Hospital?
Which tool would I use to be able to do this?
As commented by @MichaelMiles-Stimson:
Use Near from the towns to the hospitals which will give you a distance to the closest hospital then you can sort the table by near fid (the id of the closest hospital) and by distance. If you have a lot of hospitals I recommend summary statistics to collapse to a single entry by distance then relate that to a town.