If you want to really learn how to move your body (and just various parts of it), try bellydance
While I'm a musical person, I've never been a particularly good dancer. I always dreamed of doing some kind of beautiful physical art form, like ballet, but don't have anywhere near the body for it. Then I discovered bellydancing. Aside from the art itself which I am now completely addicted to, it definitely helps with feeling the music and moving your body.