I don't think there's a good answer to your question, because this is an area where different speakers differ in complicated ways.
There's a Monkees song with the line, "Mary, where're you going to?", which to me sounds very awkward at best; I would always say "Where're you going?" (There are other cases, though, where "where […] to?" does sound fine to me. For example, the complete question "Where to?", meaning roughly "Where do you want me to take you?", is much more natural than simply "Where?".)
But conversely, I find "Where are you at?" perfectly natural (albeit informal), and when I went to college, I was surprised to discover that students from other parts of the country found it very strange.
For the sentence that you quote,
It was presented to the Faculty of Arts, University of Athens where he transferred and completed his bachelor's degree.
I have problem with "where he transferred" — there's no need for a to — and I have no problem with "where he […] completed his bachelor's degree" — there's no need for an at.
But I find the full compound clause "where he transferred and completed his bachelor's degree" to be awkward, because it seems to be simultaneously using the word where in two different ways: both as "to which" and as "at which". But given the variation I mentioned above, I would not be at all surprised to hear that there are other speakers who find nothing strange about it.
(Full disclosure: although I grew up in the Midwestern US, my family spoke both English and Hebrew at home. Since Hebrew consistently distinguishes "to which" from "at which", I may be more attuned to the (potential) distinction than monolingual speakers, and this may be part of why I find your sentence awkward. But since plenty of people say "where […] to?" or "where […] at?" in various contexts, it's clear that many monolingual English speakers find a distinction natural, too.)
This variation, by the way, seems to be specific to where; at and to are basically never used with the related adverbs here and there. It's also mostly specific to at and to; I'm fairly confident that no one would object to from where, from here, and from there.