Yes, the plugin does support sorting by Distance, Store Name, Cities, and States, Admin user can setup the sorting attribute through ASL Settings. The distance sorting will work once the user sets his geolocation while the rest of the three sorting works from the start of store locator.
Sorting can also be set by the shortcode attribute sort_by, the complete shortcode will be as follows.
The valid values for sort_by attributes are "title", "city", and "state". The default or empty value will be distance sorting as provided below.
[ASL_STORELOCATOR sort_by=""] or [ASL_STORELOCATOR]