大学で勉強をしたいです。
Here, 勉強{べんきょう}
is a noun, and したい
is the verb being acted on it, so you have something like, "At university I want to do study." However, this direct English translation is a little ungrammatical, and the original Japanese isn't. So, with a little flexibility, perhaps we can capture the Japanese meaning with something like, "At university I really want to do some study!" By acting on the noun with a separate verb, it holds it up for emphasis.
大学で勉強したいです。
Here, 勉強{べんきょう}
is made into a verb by attaching したい
directly to it without the を
particle. It becomes, "At university I want to study." This would most likely be the preferred way of expressing the idea.
Depending on the context in which you were speaking, 勉強をしたい
could work, but if all you want to express is your desire to study at university, 大学で勉強したいです
is the more natural of the two.