Having grown up in the church, I have honestly never found a good replacement for the sense of community and support that a church offers. Its a shame that no other non-religious organizations have been able to replicate it.
Many parents assume kids get all the education for life in school. Teachers assume kids get most of their life education at home. This is not true all of the time but I've seen it far too often. The result is a lack of education and guidance for children. Some parents just don't have time for their kids, kids are left to learn on their own or from their environment, which is always less than optimal (yes, always exceptions to everything).
Colleges could offer credits for people who help staff and organize these places. Adults who were helped by these community centers could be encouraged to give back if it helped them in life.
Children in need of mentors should be the main area of focus in my opinion. They could call upon these people later in life if needed, almost like another parent (which not all people are fortunate enough to have). The children who were mentored would have a much higher chance of ensuring their mentor was taken care of later in life, when the mentor got old. There's just no downside from what I can tell, it's mostly a funding and organizing problem to solve.
Please don't take this the wrong way but excluding God from these centers would be important. Not everybody accepts that there is some magical being controlling everything, and many people have different gods. All of these people should be equally welcomed into community centers without fear of having God, Jesus, and the sins of the Devil preached to them constantly.