WOW. Good spot. I had completely missed that myself.
To save others a bit of digging, this one TNG episode features 3 characters who, according to their files (at least one of which is shown on screen as well as quoted in dialogue), graduated from Starfleet Academy but not from the campus on Earth.
So there are Starfleet "Annexes", or satellite campuses from which one might graduate, on Psi Upsilon III, Beta Ursae Minor II, and Beta Aquilae II, at least.
This actually solves a pretty major problem.
See, Gene supposedly thought that all Starfleet officers went through Starfleet Academy. The show has never contradicted this.
But if Starfleet has more than a handful of ships, this starts making Starfleet Academy unreasonably huge. Starfleet Academy
must produce enough graduates each year to replace all the officers who retire or die.
Let's just plug some estimates into that equation to show what I mean.
Let's suppose that the average Starfleet career is 40 years. So the average Academy graduate will serve for 40 years before he retires or dies.
Lets also suppose that the average Starfleet ship has a crew of 500, and 100 of those are Officers (and thus Academy graduates).
As a final supposition, suppose Starfleet has 4000 ships on active duty.
That works out to 400,000 Officers, 10,000 of whom die or retire in any given year.
West Point, the US Army Academy, has a graduating class of 1000 each year (meaning only 5 of 6 freshmen graduate).
The University of Iowa has 30,000 students at any given time, including those pursuing post-graduate degrees.
In 1987, the University of Connecticut admitted 2500 freshmen, which was much more than usual.
So, Starfleet Academy would need to be four to ten times the size of a modern university.
Try some different numbers:
30 year career, 200 officers per ship, 12000 ships.
That gives you 80,000 new officers every year.
But if Starfleet Academy has full campuses on multiple worlds, ... not only do the graduating classes get down to a manageable size (say, 5000 on Earth and 2000 at each Annex), but you can also have people who graduated the same year who never met each other. I mean, there were probably people in my high school class I never met (176 people), but ... well, I'd remember someone like Data. Or Worf.
As to the question: I'd guess that Starfleet offers to put an Annex on any member world, but not all of them accept. IMO, Vulcan probably doesn't have one.
http://memory-alpha.org/en/wiki/Daniel_Kwan