Hello,
Shannon gave a nice description of the different part of a traditional neuron.
Overall, the input zone of a neuron includes the dendrites *(with the axodendritic synapses) and for multipolar neurons, the soma (with axosomatic synapses). Structurally, it means that the membrane of the dendrites and the soma express many gated channels except the voltage gated sodium channels and the voltage gated potassium channels involved in the triggering and regeneration of the action potentials. However, all the other gated-channels are going ot play an important role to trigger the graded potentials (typically post synaptic potential or receptor potentials).
While the axon is the conducting zone, where action potentials are generated, you may have heard that we could have axoaxonic synapses involved in pre-synaptic inhibition or facilitation. This is when a neuron modulates an existing synapse by allowing more Ca++ to come inside the presynaptic terminal knob or less, thus modulating the number of synaptic vesicles that will fuse with the presynaptic membrane and release a neurotransmitter into the cleft. In those modulation situation, one could say that a neuron can receive signals at the most distal part of its axon.
Would be glad to help more if you wish!
severine