There are exceptions to Universities=Democratic of course. But most of those tend to be (white) universities in deep south states where the white vote is very Republican--thinking of Oxford, Starkville, Tuscaloosa, and historically College Station here. Private schools often sometimes have their own peculiar inner culture that can lean conservative, like Hillsdale or Liberty.
The Utah universities are also exceptions. Most of them are in solidly red precincts, and the ones in Cedar City and St. George are in precincts that exceed Trump +30. The University of Utah in SLC, while blue, votes well to the right of its surroundings (there's a Biden +21 precinct surrounded by precincts that are all Biden +50 or more).