The University of Goom (also known as U Goom) is a university mentioned in Paper Mario: The Thousand-Year Door. Goombella attended this college at some unknown time prior to her adventures with Mario in and around Rogueport. Her teacher was Professor Frankly, who was doing research in Rogueport during the events of the game. The exact location of U Goom is unknown.
Kolorado, the Koopa archaeologist from Paper Mario, was also one of Professor Frankly's students. As such, it is likely (although not confirmed) that Kolorado attended U Goom. This would also imply that the university was not strictly a school for Goombas.
Goombella's statements towards the beginning of Paper Mario: The Thousand-Year Door imply that she had only recently arrived in Rogueport, seemingly confirming that U Goom is not located in the rogue-filled city. However, Goombella actually describes herself as "a student in Rogueport" on the official Paper Mario: The Thousand-Year Door website, suggesting that she had not yet graduated and that the University of Goom is located in Rogueport, or that U Goom has off-campus classes in Rogueport. In Paper Mario: Sticker Star, there's a piece of paper in Shy Guy Jungle that says: "Observations on the Ancient Civilization of the Chomp Ruins" University of Goom. Goombella