What was the name of the concept based on the belief that state and local government along with private charities should decide which social programs were needed in their communities?

The concept you are referring to is often called "devolution." Devolution emphasizes transferring responsibilities for social programs from the federal government to state and local governments, along with encouraging private charities to address community needs. This approach is based on the belief that local entities are better equipped to determine and manage the specific needs of their communities.