Ah, I was fooled once again by the et at the end of Universitet.
Mot instead of till?
It works as a sentence, but there's a slight difference - it would mean "I run towards the university." Of course, that's often the same thing - but not always.
What about running the university?
The closest is probably driva, although that only really works for companies and Swedish universities aren't private. So there's no exact equivalent.
When it says "till" doesn't that mean "I run TO the university"?