In which part of a neuron is the postsynaptic membrane usually found?

Dendrite

Postsynaptic membrane is usually found in the dendrite.

Dendrite is the primary site on a neuron for receiving signals from other neurons and it transmits the signals toward the cell body from which the dendrite extends from, using short distance graded potentials rather than action potentials. In a chemical synapse, the postsynaptic membrane receives a signal from the presynaptic cell and responds through depolarization or hyperpolarization. The synaptic cleft separates postsynaptic membrane from presynaptic membrane