I don't know why I am so dumb that I spent so much time scouring the Web to look for a utility to convert between different audio file formats. In fact my favourite video player, VLC can do it right under its hood.
Why would I want to do this conversion business? Because I have a bunch of WMA files which I can't import into my iTunes (but it works on M$ Windows though).
The weird thing is that I didn't manage to coerce VLC to convert it to MP3 for me so in the end I just did MP4 anyway since iTunes support it.
Here are the steps that you need to take:
- Start up VLC
 - Click File and select "Streaming/Exporting Wizard..."
 - Select "Transcode/Save to file", click "Next"
 - Select a file and click "Next"
 - Check the "Transcode audio", and select "MPEG 4 Audio", select the bitrate that you want and click "Next"
 - Select "MPEG 4/ MP4" and click "Next"
 - Choose a filename and path to store the new file and click "Next"
 - Click "Finish"
 - Wait for it to be done
 
You can also choose other audio file formats and its pretty easy. Although I wish there is a better interface for this.