AsyncTask for subscribing to current location
Note: the following refers to native Android development, I am not familiar with xamarin.

About the approach
It depends on what your aim is. The downside of using AsyncTask is that it's tied to the Activity you're calling it from. I recently implemented continuous location tracking, where AsyncTasks were not an option, as the process of continuous tracking is not tied to a particular activity. So I opted for an Android Service implementation instead. The Service was in it's own class and while you could bind to a service in a given Activity I instead went for the EventBus pattern (there are other options though) - meaning every time the LocationService obtained a new location it would cache the most recent location and propagate an Event via the Eventbus. This way subscribers (such as Activities) would be informed of location changes and could update the UI accordingly.

However, if you only want to query for locations within the Map Activity, then an AsyncTask may in fact be enough (I would put that in a separate class file though so it's reusable). The downside of this approach is, that since you only start asking for locations once you enter the Map view, it may take a moment to obtain a viable location.