Translation:Her apartment is far from her university.
You need to understand the context in this case
For me, Japanese, seeing this sentence and feel like "why would someone talk about other school when we are talking about the specific person "her", it must be the school where she always go."
Yep context is very important im Japanese
The closest thing to the word 'uni' in Japanese is 'dai' (大). But you wouldn't use it in the same way as we use 'uni' in English.
University of Tokyo -> Tokyo Uni
東京大学 ー＞ 東大
This works in both English and Japanese. But you couldn't say "I go to uni." in Japanese. Only "I go to university".