ArcGIS Server 10.2 lets you review service workspaces for each service in ArcCatalog and Manager (http://resources.arcgis.com/en/help/main/10.2/index.html#/Reviewing_service_workspaces_in_Manager/01...
I suggest the following:
a) Information on service workspaces should also be accessible through the Admin API
b) It would be nice if we could also go the opposite way, i.e. start from a workspace (/arcgis/admin/data/items/enterpriseDatabases) and find all services that use it.