If you have Firefox all you need to do is add the youtube to mp4 add on...once it is added there will be a "Download as MP4" link right below the Embed Code then you just choose Save As...then go to google and download the m4a to mp3 converter from maniac tools for free then set it up to the bit rate you want and choose convert and it will convert to mp3.
Also, Firedownload add on for Firefox will greatly increase download speeds, even on my very fast work connection it takes like 3 minutes to download a 9mb mp4 from YT but when I use the Firedownload it dl's in about 5 secs...just be sure when downloading from a site that uses a wait time like zshare or rapidshare, etc just uncheck the FireDownload box before saving