Depends what is available in your area.
Swimming, musical instrument and martial arts are all goo suggestions as above.
Also, what about drama, dancing, scouts or guides, athletics or other sport, join the golf or tennis club, helping out at the local kids football team training, camera club etc.
It is worth seeing what is available through your council, local arts centres, community centres, churches (you don't have to be religous) and schools. There are alo lots of professional companies that run youth drama groups etc.
You just need to hunt about and also ask your daughter what activities her friends do.
Hope you get something suitable. I think you posted before about her being shy, maybe a performing arts class might boost her confidence - if you can get a friend to go as well that may help. Try lobbying her friends first and they may persuade her better than you can.