There are basically two scenarios where Async/Await is the right solution

I/O-bound work: Your code will be waiting for something, such as data from a database, reading a file, a call to a web service. In this case you should use Async/Await, but not use the .Task Parallel Library

CPU-bound work: Your code will be performing a complex computation. In this case, you should use Async/Await but spawn the work off on another thread using Task.Run. You may .also consider using the Task Parallel Library