I'm late to the party here, but there's an awesome library I've been using which I haven't seen referenced in the other answers
https://github.com/brminnick/AsyncAwaitBestPractices
If you need to "Fire And Forget" you call the extension method on the task.
Passing the action onException to the call ensures that you get the best of both worlds - no need to await execution and slow your users down, whilst retaining the ability to handle the exception in a graceful manner.
In your example you would use it like this:
public string GetStringData()
{
MyAsyncMethod().SafeFireAndForget(onException: (exception) =>
{
//DO STUFF WITH THE EXCEPTION
});
return "hello world";
}
It also gives awaitable AsyncCommands implementing ICommand out the box which is great for my MVVM Xamarin solution