You can either go by bus or by taxi.
You can go either by bus or by taxi.
I think the first is wrong and the second is right, for there is parallel struction.
Am I right?
You are right that example 1 does not comply with parallelism. For clarity, I have bracketed the phrases separated by or of the correlatve conjunction pair.
You can either [go by bus] or [by taxi].
You can go either [by bus] or [by taxi].