YouTube to MP3 conversion is not the sole purpose of the program, so it's rather larger than you might expect, but this should not put you off (but take care not to install the optional adware during setup). While this is part of what it can do, it can also be used to download videos from YouTube and save them as MP3s – exactly what we’re looking for!
You would be forgiven for judging Any Video Converter Free by its name and believing it to be a tool for converting from one video format to another. If you're looking for a fast, flexible YouTube to MP3 converter, this is the tool for you.