When my safari was working on my mac, I would go into the activity window and download the youtube video into a file directly onto my desktop. I also use a website called keepvid.com or viddownloader.com. Viddownloader allows you to save the file as .avi file and keepvid downloads the file to .flv format.
For video conversion I always use an app called VisualHub. VERY useful. You can change almost any file into any other file including audio.
Also, I use wiretap pro to record audio to mp3. Wiretap pro can record the mac system audio or even use the built-in microphone. When I don't want to open up garage band, I just use wiretap pro to make a quick mp3 then if anything needs to be edited i use quicktime to do simple editing.
Even better still for mac users... If you have Quicktime pro, you can open up any movie file (including .flv files with the updated codecs so no conversion is necessary) and go to window>Show Movie Properties. You can see the video track and the sound track and there is a button that says "extract" you can extract the sound track of the video file and then export it into several different types of audio.
Also, for mac users who love youtube, you should check out tubesock.. For tubesock, all you need is the youtube URL or the video ID and it downloads the file automatically and converts it into a whole bunch of different video formats OR it can save it as an mp3 of the video file. It can also import the video or the audio directly into itunes.