Exercise is important for everyone. Take him on a daily nature walk. The two of you can exercise together and explore. Take a digital camera, let him take pictures, and at home he can paint the different species of birds, plants, wildlife, etc. that were discovered. Bring home leaves and do leaf rubbings. Collect rocks. You can explore different parks and nature trails, as well as your own neighborhood. Count the number of birds you see, find things that begin with the letter A. Race to the next object of interest, help him climb a tree, dig for an earthworm, swing on a swing and feel the wind on his face, go fishing, look for shapes in the clouds. When he starts feeling safer in these activities bring a friend of his along.
Regarding developing an interest in music, we would listen to classical music and make up a story with the tempo of the music. My children both love music and have fond memories of our stories. I would also surprise them and turn on the stereo LOUD, they would come running and we would dance around the house together.
My son was very much like yours and we had to be creative and help him discover how fun it is to try new things and explore and investigate God's world. He never did care for organized sports, but he did try it. He is now very scientific, very creative (enrolled in College and entrapeneur in graphic arts), but he also likes long boarding, golfing, fishing, playing in a band, and other activities. First, we had to show him how much fun it could be, plus it was great bonding time for us as a family.