I don’t know about your area, but a lot of the schools around here have “Heights” in their name, because the towns have “Heights” in the name (Arlington Heights, Prospect Heights) and the schools are named after the towns.
With the exception of Siena Heights University (it was College until 1998), all the “Heights” schools that I know are in towns named ____ Heights, but most of those are named for the cachet that accompanies the name. Generally, the “working” town is down on the flatland or in the valley while the rich folks get to live on the hills above (where they have a better view and where, in the days of wood and coal-fired heating, they were not stick in the miasma of smoke). While some early towns were named ______ Heights simply because they sat on hills, many of those attracted the richer people for the reasons given above. Following that (I would guess) some schools decided to tag the word Heights onto their name to give the appearance that they were associated with the upper crust.
(Siena Heights was named for St. Catherine of Siena. My guess that the “Heights” was (ostensibly) recognizing that it was on a (sort of) hill on the outskirts of Adrian.)
“Heights” must be an east coast thing. In these parts (So-Cal), the snooty towns add “Hills” to their name instead – i.e. Beverly Hills, Agoura Hills, Granada Hills, etc.
Most egregious use = the town of Sepulveda, best known for its dive bars and strip clubs, decided to revamp their image by changing their name to “North Hills” – ignoring the fact that the town’s located in the exact CENTER of the San Fernando Valley and is miles away from anything resembling a “hill”!
A lot of mid-fifties and sixties Ontario suburbs were named with ‘Heights’. In Peterborough, there are 'Edmison Heights" and ‘Kawartha Heights’, for instance, and they are located on hills, so you get the classic well-off suburban sloping street with a view. Around here I don’t know of any towns named with ‘Heights’ though.
I know why "Springfield Heights Institute of Technology (Apu Nahasapeemapetilon’s alma mater) has Heights in its name, but I can’t help you with other schools.
For what its worth, none of the schools where I live are named _________ Heights. There are names for local politicans, presidents, the general area, historic places and ideas, the containing town or city, rivers, mountains, and other geography, but no _____ Heights.
Perhaps it’s just a local thing. Many schools around here are “Heights” and there are no obvious corresponding hills, mountains, etc. Maybe it is the “snob” factor, too.
One other factor to consider for the Eastern and Midwestern US. Even when there are no obvious large hills or ridges around, in the ninteenth century, many schools and hospitals were located on whatever bits of higher ground was available. Before tuberculosis was TB, it was “consumption.” At that time, one of the prevailing beliefs about consumption was that it was caused by “unhealthy air”. Hence, building hospitals and schools on hills to get the patients or children up and out of the “bad” air. See, for example, St. Elizabeth’s Hospital in Boston.