Hi,
My daughter is 10. We're not a very athletic family, although she has participated in summer programs (usually one week at a time) for soccer and dance with limited enthusiasm. During the school year, I like her to have free time after school. I've spent a lot of time in the classroom as a volunteer and it's not like when I went to school. They have a LOT of material to cover and it's pretty fast-paced. After a full day of that plus 45 min - 1 hour or so of homework, she's ready to have time alone or play wii for a while to unwind before dinner.
My husband gets home from work around 6 and we all sit down as a family to eat dinner. It keeps us connected and I feel it's really important to have that face-to-face time. FYI - kids who eat REGULAR meals with their family are statistically less likely to smoke, drink, do drugs or engage in risky behaviors. That said, my daughter has taken guitar lessons and more recently horseback riding lessons (1X per week through late Fall). We may start that up again in the Spring since she really liked it.
We spend a lot of our free time at church. My daughter will sometimes attend a kids' Bible program on Thursday nights while the adults have their own study at the same time. On Sundays she attends Sunday school while we're at regular service. Next year, she'll get involved in Youth Group which I'll also be involved in. There's also a special girls' Youth Group that focuses on purity.
On weekends when the weather is warmer, we go to the park, spend time visiting family or sometimes do a day trip. Lots to do in NJ & NY. We like having free time on the weekends. I could never be a soccer Mom and be tied into a schedule of practice/games/traveling teams, etc. Just not my thing.
I understand that most kids enjoy a lot of activities. I believe you should allow your children to explore different activites to see what they enjoy and/or what they have tallents for. Just my opinion here, but I think there are a lot of activities that reel you in for big bucks when the kids don't really need to make a career of any one thing. I also think life is stressful enough for our kids when they grow up. They shouldn't be scheduled every minute of every day and/or expect to be entertained all the time or have an organized activitiy all the time. Just my 2 cents. Good luck - good question!