I am close to the river = this is fine
I am close by river = this is wrong - you can't say this
My father lives quite close
My father lives quite close by = there is no difference between these two
'Close to' needs to be followed by something: you have to say WHAT you are close to. 'Close by' is an adverbial phrase, so it can stand alone.
John lives close to the station.
We're at the station now, so his house must be close by.
it's the same as:
John lives near to the station.
We're at the station now, so his house must be nearby.