According to The Chronicle of Higher Education:
In the counties that are home to public flagship universities, only nine favored Donald J. Trump over Hillary Clinton, according to a Chronicle analysis of voting data. In the 49 counties included in the analysis, Mrs. Clinton beat Mr. Trump, on average, by about 18 percentage points. In counties with a public flagship, the percentage of voters favoring Mrs. Clinton was 11 points, on average, higher than her statewide percentage.
Alaska was excluded from the analysis because it does not have county-level election data from the 2016 presidential election. Some states have more than one campus that serves a flagship role; to keep the analysis simple, we selected only one from each of the other 49 states.