You can assume that any Large City (population 10.000-25000) or larger city should have a magical academy, but most of them arent famous enough to be worth noting. Most academies become famous due to their students becoming celebrities as powerful mages themselves.
Most known Capitals do have the academic settlement quality, which means the city has a place of study of some sort, magical or not.
According to PathfinderWiki.com on the subject of Magic Schools, we have the following:
The Acadamae, the premier magical college of the Varisian city of Korvosa, holds an annual event called the Breaching Festival.
Abjuration is also one of the chief focuses of study at the Stone of the Seers, Magnimar's best-known academy of magic.
At The Acadamae, Korvosa's premier magical institute for the instruction of specialist wizards, conjuration is favored over the other eight schools of study and is a required component of every student's final examinations.
Conjurers, especially if they are also diabolists, find considerable favor in Cheliax. Living in a country where the state religion is the worship of Asmodeus, Cheliax's citizens tend to respect all arcane spellcasters due to their assumed connections to Hell.
Other groups known to deal with conjuration include the opposing Blackfire Adepts and Riftwardens, the Irriseni Bloodstone Conservatory, genie binders, Hellknights, Nidalese shadowcallers, and Osirian mages.
Diviners are often found in the company of leaders and the military, as their magics allow them to glean information about enemies and discover the presence of spies, assassins, or plots against them. Pharasma, the goddess of fate and prophecy, is the patron of diviners.
With the advent of the Age of Lost Omens (death of Aroden) over a century ago, the reputation of diviners and soothsayers has been diminished.
Elven minds seem to be particularly resistant to enchantment magics. The god Asmodeus is associated with enchantments and enchanters of all kinds, and is often worshiped by the less wholesome ones.
At the premier arcane school of Varisia, the Acadamae, evocation is the second-most popular specialization after conjuration.
The lesser-known goddess Sivanah, also known as the Seventh Veil, is considered the patron deity of illusion magics, using it to cleverly conceal her own appearance under layers of obfuscation. Illusionists can be found as priests of her church, although those with different personal or philosophical outlooks can also be found among the clergy of Calistria or Norgorber.
Some of the most well-known necromancers the world has ever known were undead creatures themselves, such as the archmage Geb, and the dreaded lich known as the Whispering Tyrant. The goddess Urgathoa is the patron deity of many necromancers, although some also worship the lesser-known demon lord Orcus.
Although they can be found throughout the world, the arcane schools of the Garundi nation of Geb specialize in the teaching of necromancy. One of the most notable is the Ebon Mausoleum in the capital, Mechitar.
Among the Varisian people, this type of magic is known as "avaria"
The ice mages of Irrisen are known to be focus largely on transmutation spells, especially those that deal with manipulating all forms of water.
The wizards of the land of Nex are said to have a strong preference for this form of magic.
Arcanamirium The largest and most respected school of arcane magic in the
Inner Sea region, established by exiled arclords of Nex, focuses
on the study of practical magic. Location Absalom.
Magaambya Founded by legendary wizard Old-Mage Jatembe, this is the oldest surviving and still operating academy in the Inner Sea region. Location Nantambu (Mwangi Expanse).
Kintargo Opera House Growing swiftly and welcoming non-Chelish students, this Chelish opera house is building a dangerous reputation for fostering free thinkers. Location Kintargo (Cheliax).
Oenopion Fleshforges Strange new soldiers are alchemically and magically constructed in the experimental laboratories of the Oenopion Fleshforges. Location Oenopion (Nex).
Poisoner’s Guild One of Daggermark’s most powerful and notorious guilds, the Poisoner’s Guild is led by Tragshi the Herbalist. Location Daggermark (River Kingdoms).
The White Grotto is the premier bardic college in Absalom, a guild where one can learn the arts of using magic to enhance all forms of entertainment. Location Absalom.
Citadel Enferac The stronghold of the Hellknights of the Order of the Gate, Citadel Enferac is one of the primary locations at which Hellknight spellcasters (known as signifers) of all orders train. Location Menador Mountains (Cheliax).
The Harrowed Society Based in the town of Galduria, the Harrowed Society uses the Twilight Academy as a sort of “ front” for their true purpose: to decipher the mysteries held in harrow cards, the traditional Varisian fortune-teller’s tools. The Harrowed Society believes that if these mysteries can be deciphered, the true secrets of reality can be learned. Location Galduria (Varisia).
Crimson Citadel The Crimson Citadel is the headquarters of the Red Mantis
assassins, deadly and mysterious killers who worship Achaekek the Mantis God. Location Mediogalti Island.
(References of academies, secret societies and guilds taken from Inner Sea Magic.)