I was luckier than I deserved. I pretty much chanced into going to UIUC, which was home to an NCSA supercomputing center and thus was directly on the NSFNet. So not only did we have internet, but it was mind-blowingly fast.
The university was connected via 1.5Mbps T1 when I started, soon upgraded to an ultra-luxurious 45Mbps T3. Let me stress... this was for the entire university of 35K+ students.