Cooper Union has not charged tuition in my memory. It was, and is I believe, an excellent school of engineering and architecture. It may heve incorporated the arts asplaces like Parsons School and the New School have also done. I believe the funding is privately endowed. It was at The Coope Union that Abraham Licoln made his most famous pre presidency speech. I guess the standards in oratorical guests have fallen quite a bit since 1860.
According to Cooper Union's website under "admissions" they accept federal Pell grants and private grants. (As far as I know only Hilldale College in Michigan is 100% free from federal money and 100% private. Does anyone know if that is accurate?)