Music: I used to play the slide trombone, now I blow my harmonica sometimes. I can't play properly, I always mess up the string of the notes, maybe it's my ADD, what a pity. I listen to recorded music instead, excessively.
Excercise: Cycling (and commuting), swimming, regularly. Garden sometimes. Tinkering with audio equipments is rather an interest or passion than exercise.
I also arrange things with myself by bringing up ideas and concepts in my mind, thinking of past events, how they fit in, and what are their possible interpretations.
I think exercising the mind is always good, it has a positive impact on the skills. Also, for everybody, not only for those on the spectrum, physical activity is always recommended.
When I feel anxious, feel excessive energy, redirection to useful activities, such as unfinished projects (which I have many), might be beneficial, or even the only right way to help reducing my anxiety to a bearable level.