Neuron's do indeed have mitochondria. Aside from glucose they can use ketones (ketone bodies) which are produced in the body where there is a lack of glucose. In theory they could use FFAs but they do not cross the blood-brain barrier very easily as they are normally bound to plasma proteins.
RBCs need glucose only as they have no mitochondria, the reasons being explained above. All cells need glucose for normal metabolic processes such as cell repair etc.