Well, to begin with, even the tender ride in is great; it's a beautiful bay with great vistas. Then the bus ride up to Taormina is spectacular with beautiful panoramas all around.
The town itself is something right out of a fairy tale: cobblestone streets, window boxes with flowers, cafes, shops, friendly people. One of the highlights is the 2nd Century amphitheater that has been restored and still used for concerts today. And the views in every direction are nothing short of spectacular.
I think instead of "what's there to do in 6 hours?", the question should be, "can I stay longer?" :-)