No, keep it. It's not clear if "wasn't" refers to "I" or "there"(the university?). It sounds like broken English if you omit the second pronoun. Also, "campus" probably isn't the word you mean. That word means the physical area of the university.

I also had fun with the students, even though I wasn't from their campus. (From there is grammatically incorrect)

"I had fun hanging out with some students from that University but I wasn't studying in the same University with them".

Wikipedia: A campus is traditionally the land on which a college or university and related institutional buildings are situated. Usually a college campus includes libraries, lecture halls, residence halls, student centers or dining halls, and park-like settings. The meaning expanded to include the entire institutional property during the 20th century, with the old meaning persisting into the 1950s in some places (emphasis added). Dictionary.com: Campus: 1. the grounds, often including the buildings, of a college, university, or school (emphasis added). 2. a college or university [e.g., The large influx of older students radically changed many campuses throughout the country.] Oxford English Dictionary: Campus: The grounds and buildings of a university or college (emphasis added). (e.g., For my first year there, I had a room on campus.] During the entirety of my lifetime, those words have been synonymous, thus, you can, and should, use campus to mean a university or college without any reservations. While I am an American, the entry from the OED indicates that it is true “across the pond” as well. Sorry, I do not have an icon next to my name, and so, the reason I provided the sources above… (and although I italicized my "emphasis added" text, it does not show in the above...)