Either or neither: a pair that many people seem to be confused about. So let’s sort this one out.
The main rule for this is quite simple, and there are some stylistic points, too.
The basic idea is that either is followed by or, and neither is followed by nor.
So, “Either we’ll go to the cafe or we’ll go to the pub”, “They went to neither the cafe nor the pub, but had a walk in the park, instead.”
It is incorrect to write: “They didn’t go to either the cafe nor the pub”, or “They went to neither the cafe or the pub”. Quite simple: either … or and neither … nor.
Stylistically, both kinds of sentence need to be balanced: so you wouldn’t say “either we’ll go to the cafe or the pub” or “He neither saw himself as farmer or politician”.
Confusion also sometimes arises with the use of or/nor with no and any. “No people or pets were harmed during the filming”; “we did not harm any people or pets”, not “No people nor pets”; “any people nor pets”.