B.D.
My daughter is 9 (going on 10 very soon). Homework does not consume more than 30 minutes a night. Most days I ask her to get some reading in but that is in lieu of watching tv.
She too is involved in sports, Girl Scouts, CCD, etc. I see that as her 'socializing' time. In the summer time she will do our community's recreation program where she will get to see and play with her friends 3 hours every morning 5 days a week. In addition she does have a 6 (almost 7) year old sister who she gets along with very well. So they will often play together. Therefore I do not schedule playdates too often but am willing to if I feel or see that it is necessary.
As for wanting to 'hang' with the adults...I completely get it. My daughter is much more mature than her peers so she often does gravitate more towards 'adult' conversations. For example over the summer I noticed that a lot of times at rec she would rather to talk to the college aged counselors than to run around with her friends. I was taken back by that until a friend (and teacher) told me that that is normal based on her maturity level.
You know your daughter and her needs best so do what you feel is necessary.