It would be the first one. You say you're going to use the instrument available (meaning "able to be used or obtained"), then specifying the location it can be obtained from: inside the university. (you could also use "from" here, which would sound more natural).
Your second sentence has two possible interpretations: one is that you'll use an instrument which can be obtained next to the university (using "by" as a locative, which is obviously not what you want); the other interpretation is that the university (in this sense talking about its faculty, not the building itself) allowed you to use it, in which case you need an active verb to clarify this, so the sentence would be:
We are going to use the instrument (which was) made available by the university.