Directed to the OP:
Don�t let the well-intentioned, but ill informed, bother you. �Hanging out� is normal for any teenager, and the fact that you asked specifically for a kosher way to fulfill your desire for camaraderie is laudable.
There are many places where girls can go and �chill� and it doesn�t need to be to another shiur or �chessed project�. Go bowling or ice skating or sit on a porch with a slurpee. Find a good kosher coffee house or art gallery (that your parents approve of� art can be great when not inappropriate).
The unwillingness to accommodate isn�t from das Torah, it�s from people who are too afraid to ask an open shaila. I�ve spoken to many great gedolim including several just last week while in Eretz Yisroel; a big yetzer hora of this dor is to asur everything to the point of causing resentment and anxiety.
Go chill, hangout, relax� in a kosher, yosher way. Make sure you have solid Moros to guide you. Hatzlocho!