The LocalLocatorTask class was included in previous versions of the ArcGIS Runtime SDK for .NET, most recently at 10.2.7.1234. It was extremely helpful to have offline geocoding capabilities in certain apps.
This class has been removed from the newest version 100.0.0. The Esri.ArcGISRuntime.Tasks.Geocoding namespace can be viewed here.
Why was that class removed and is there an alternative operation we can use for offline geocoding?
It wasn't removed. They just converged. You'll just use the LocatorTask, but instead of using an online Uri, you use a local uri. Ie
var task = new LocatorTask(new Uri("file://c:/data/mylocator...");