teenager,
I am not a teen but I have a question for you. I am trying to undersand why you and your friends hang out in bad places and do bad stuff. Is it because you are bored and therefore having a kosher hangout will simply get rid of the boredom and completely solve the problem, or is it that you all have other issues (I think you mentioned that you were abused – that is awful and I feel terrible for you) and you feel a need to rebel to let out your pain. If this is the case, then I don’t see how a kosher hangout will solve anything. Suppose there was 3 hours on motzai shabbos of bowling, pizza and interesting shiurim etc. After it ends would kids just go home or would they head straight to 7-11 or wherever else they currently hang out? I am not trying to knock your suggestion, just trying to understand it better.
I think a better solution may be for you individually to find an older adult you can respect and confide in. From your response to smartgal you seem to crave that. Maybe the rebetzin of a shul? Maybe a teacher you once had, whether in elementary school, high school or seminary. Maybe a neighbor or a friend of your mother? Maybe project yes can find you someone? Maybe smartgal?
It would seem to me that this would get to the root of the problem more than just being kept busy for a few hours in a kosher environment. Am I making any sense?