M.W.
I highly recommend gymnastics. It's a great basis for any sport because you learn coordination, balance, strength, and listening skills. I coached gymnastics for 6 years, and now my 7 and 4 year olds are involved. My 7 year old is on the team. She started when she was 3 years old. Gymnastics is something you have to start early in to be any good at it, but there are still benefits to starting later. I think they get over the shyness after going for a few weeks.
Another idea is some sort of music lessons.
Although I do value kids having down time, many kids have too much of it and spend too much time watching TV and playing video games.