Motor neuron disease is, as the name says, a disease of motor neurons, and the classic form is amyotrophic lateral sclerosis. It strikes both layers of the motor system: the upper motor neurons running down the corticospinal tract and the lower motor neurons.
The question wants the spinal site, and that is the home of the lower motor neuron cell bodies, the anterior horn of the gray matter. As these cells die, the muscles they supply waste away, twitch with fasciculations and grow weak. Mixed with the upper motor neuron signs of spasticity and brisk reflexes, this gives the characteristic combined upper and lower motor neuron picture.
A defining negative is that $sensation$ is untouched. That single fact lets us discard the sensory options at once. The spinothalamic tract (pain and temperature) and the spinocerebellar tract (unconscious proprioception) are both sensory and stay intact. The peripheral nerve belongs to neuropathies, not to the core lesion of MND.
So the answer is the anterior horn cells.
\[\boxed{\text{Anterior horn cells}}\]