Bible translations are made from sources. Where are these sources? In a university, museum, government agency or what?
The short answer to the question is: in museums and libraries throughout the world.
The sheer number of fragments alone means that no one academic entity - let alone even one government or ecclesiastical authority - can "own" them all.
There are over 5500 manuscripts, miniscules, unicals, papyri, parchments, and fragments that critical scholars have used to ascertain the authentcity of the Scriptures as we have them today. A corpus like the Nestle-Aland 28 brings together some of the best consensus from the history of the manuscripts to most definitively decide what the "original" text most likely said - and the use of an appartus will illustrate the various manuscripts that were used to make the determination.
With over 5500 manuscripts, then, a complete list is too broad. That said, there are a few key manuscripts that scholars would go to right away:
Interestingly, the oldest known fragment of the New Testament - p52, John Ryland's fragment of a verse in John - is located in library at the University of Manchester, England. There are online pictures too...