One thing I don't get is why they are so few Starfleet Academies mentioned, and every one seems to refer to Earth as the only SA. Federation territory is huge. It takes approximately 5 years to cross at its thickest points. I know in TNG, there were a couple mentioned. It doesn't make sense to have to just one or two Academies across the Federation.
Here is some maths: There are 150 planets in the Federation (at the time of TNG/DS9/VOY), and I would assume that doesn't even include their colonies. Each of them will send their kids off to join Starfleet as it's the military and scientific/research/medical arm of the Federation, and that would mean 100s of thousands of people needing to attend Starfleet training. Surely it would make sense there would be Academies on most member planets?
For arguments sake, let's say everything here is true: if there are 150 planets, and on average there are 1 billion people living on each planet, that's 150 billion people. Let's say 5% of those people join Starfleet in a 10 year period, that's 7.5 billion in 10 years they have to train, or 750 million a year.
In reality, the vast majority of member planets would surely have more than a billion people living there by the time they become a warp civilisation.
To answer, Starfleet is a primarily Human organization. It's roots are from the old Earth Starfleet and it follows in it's tradition. It was only sometime after ST6 that the Federation President was the Commander In Chief. But still, Starfleet even into the 24th century remains a majority Human. Other races join, but Humans are the backbone.
We've seem that other Federation worlds can and do sometimes operate their own fleets and intelligence agencies. (The Vulcans in particular) Many aliens may choose to stay with their homeworld fleets.
The Academy surely does have off-world locations, but they are just satellite campuses of the main San Francisco campus. Also, not everyone in Starfleet goes to the Academy. We generally only see the officers, but Starfleet does have an enlisted corps. Chief O'Brian never went to the Academy. In fact, as evidenced by Wesley Crusher's trials......getting into Starfleet Academy is HARD. MOST people in Starfleet probably did not go to Starfleet Academy, just like most people in the US Army did not go to West Point. We just generally see the senior officers of the ship, not the regular crewman in waste reclamation.
I take issue with the statement "Chief O'Brian [sic] never went to the Academy." It has been established that, either voluntarily or involuntarily, O'Brien was demoted. It is also been established that Starfleet Academy has a technical college specifically for non-officer candidates. O'Brien started out as an Ensign, then a Lieutenant Junior Grade. His "demotion" to Chief Pettey Officer was part of the "O'Brien must suffer" movement of Star Trek: The Next Generation and Star Trek: Deep Space Nine. The reason(s) for the writer harassment of the character has never been established.
It does stand to reason that the Academy does have (probably several) campuses outside Sector Zero-zero-one, including many enrolled students stationed on starships, starbases and other Federation installations.