Neighbor (noun): A person, place, or thing situated near another. From Old English nēahgebūr ("near-dweller").
"Neighbor" implies proximity and potential interaction. In topology, "neighborhood" has precise mathematical meaning. In networking, "neighbor" denotes directly connected nodes. The opposite depends on which dimension (spatial, social, topological) is relevant.
There is no single word that exclusively means "non-neighbor" across all contexts.