My contention is - not much if anything.
History. All D&D settings are full of things done by ancient wizards or whatnot that are not actually achievable by PCs or NPCs under the normal game rules, whether it's the Field of Maidens or the Mana Wastes in Golarion or the Sea of Dust in Greyhawk or everything in the Forgotten Realms and Eberron. Using E6 for your PCs doesn't change that at all, so you don't need to retcon history to only account for "sixth level abilities."
Politics, Civics. First check out What percentage of the population is magical in Pathfinder's world of Golarion? Golarion is designed to not have many high level NPCs in the first place. Only people like country leaders are listed as higher level, or super-rare exceptional NPCs like Baba Yaga. You don't actually have to use the E6 rules for NPCs, so you could keep the most notable high level folks as their real high level and just make them super dangerous to cross for E6 PCs - a foe to plan a campaign around, not a mob to grind once the party's high level. Or, you can limit those rulers to L6 and rebuild them (where relevant) using the E6 rules. In that case the only political change I can think of is in cases where humans are collaborating with nonhumans (with the giants and winter wolves in Irrisen for example), devising a more nuanced justification for their cooperation than "a high level caster would melt the giants' faces if they misbehaved." So no real politic or civic changes except challenging you to find more textured explanations than "He in charge cuz he can bash everyone else."
Economy. Economy wise, there's less to spend megagold on since there's not super expensive items - but the inflation and problems of PCs having megagold compared to normal folks isn't good or conducive to a coherent game world anyway (see How to handle wealthy player characters as a GM?). The Golarion economy works better without the "hey there's a guy with 100,000 gp worth of stuff on him" problem.
Military. No D&D setting has ever had their militaries really reflect the realities of the D&D magic and combat system. They're always medieval-based theories of troops and fortifications that fly, invisibility, etc. make hash of. So there's not much to "dumb down" - the most notable "fantasy" units in Golarion are things like the Sable Marines of Korvosa who ride hippogriffs, which is still completely appropriate for E6.
Bestiary. Obviously you'd take a lighter hand with the high CR monsters just like the E6 rules say, but you don't have to remove them all - so a Linnorm King having to defeat a Linnorm is still on the table, it just means that the Linnorm Kings are way more bad ass than just being "a high level guy."
Adventures. The main problem with E6, really, is using the adventure content for Golarion. The Adventure Paths all go way past 6th level and chapters 3-6 would require significant adaptation, including the encounter tables and all. Since a big draw of Pathfinder/Golarion is the adventures, that's really the major downside. Also, if you limit all NPCs to L6 then your capstone threats can only be "monsters," which removes legendary threats like Baba Yaga, which is a bad GMing mistake IMO.
Frankly, E6 makes Golarion make more baseline sense than the usual d20 rules do! That's a big part of its draw; Golarion like Greyhawk and most traditional D&D campaign worlds are really only coherent if you assume there's not a bumper crop of high level folks around.
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:
Abjuration
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.
Conjuration
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.
Divination
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.
Enchantment
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.
Evocation
At the premier arcane school of Varisia, the Acadamae, evocation is the second-most popular specialization after conjuration.
Illusion
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.
Necromancy
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.
Transmutation
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.
Other Academies
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).
Spellcaster Guilds
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.
Secret Societies
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.)
Best Answer
The core Pathfinder rules for settlement demographics are in the PRD. It includes information on the highest level of spellcasting available in a settlement of each size. For example, in a large town (2001-5000 people) you can buy up to a 5th level spell. Even in a 20 person thorp you can get 1st level spells. This speaks to a certain level of commonality. If you want to flesh out a whole population, the 3.5e settlement rules had more thorough coverage.
There are however more Golarion specific rules in the Inner Sea World Guide p.253. To quote James Jacobs, Creative Director at Paizo, on the intent of this section from the Paizo forums:
Also,
And
You can look up various Golarion heads of state's class/levels on the Pathfinder Wiki.