University

A University is an institution of higher learning with research and teaching facilities that awards degrees.

In 2151, Hoshi Sato taught as a university professor in Brazil, before she took a commission aboard the starship Enterprise (NX-01) as communications officer. (ENT: "[[Broken Bow")

Dr. McCoy attended the University of Mississippi in the mid-2240s, at which time he met the joined-Trill Emony Dax, who was visiting Earth to judge a gymnastics competition. (DS9: "Trials and Tribble-ations")

from Memory Alpha, the canon Star Trek wiki.

Bajor

 * Bajoran Military Academy
 * University of Bajor

Cardassia Prime

 * Cardassian Military Academy
 * Central University
 * University of Culat
 * Culat

Klingon Empire

 * Klingon Defense Forces Elite Command Academy

Romulan Star Empire

 * University of Ki Baratan
 * Romulan Intelligence Academy

Aldebaran Prime

 * University of Aldebaran
 * New Melbourne, Aldebaran Prime
 * Aldebaran Music Academy

Alpha Centauri

 * University of Alpha Centauri

Betazed

 * University of Betazed

Earth

 * California Institute of Technology (aka Caltech)
 * California, North America
 * Cambridge University
 * Cambridge, England
 * Columbia University
 * New York City, North America
 * Indiana State University
 * Indiana, North America
 * Kent State University
 * Cleaveland, Ohio, North America
 * The Makropyrios
 * University of Manitoba
 * Manitoba, Canada, North America
 * University of Mississippi
 * Oxford, Mississippi, North America
 * Monash University
 * Australia
 * University of Nairobi
 * Nairobi, Kenya, Africa
 * Princeton University
 * New Jersey, North America
 * Stanford University
 * Palo Alta, California, North America
 * Starfleet Academy
 * San Francisco, California, North America
 * University of Texas
 * Texas, North America
 * Vasteras University
 * Sweden
 * Victoria University
 * Wellington, New Zealand

Regulus III

 * Regulus III Science Academy

Trill

 * Ganses University
 * Kem'alta Institute

Vulcan

 * ShiKahr Academy
 * Vulcan Science Academy

Interstellar

 * Daystrom Institute
 * Annexes include:
 * Galor IV
 * Timsonian Institute
 * Cluster Telpha-Z

Location Unknown

 * University of Copernicus