My personal view is that there is only one Starfleet Academy.
There are other military academies that Starfleet selects new officers from (like the home academies of member planets), and there are ROTC units in a number of universities.
Also, persons with very specific skills (M.D.s and science officers) may gain a commission after completing their academic courses (McCoy had gone to medical school before getting his OTC-style orientation at SFA). The Vulcan Science Academy probably has a number of science officers among its ranks of alumni.
And, of course, you have the few mavericks coming out of the enlisted ranks (of course, I think mavericks are extremely rare, given the nature of enlisted personnel in the Star Trek universe).
So, there are a number of ways to get a commission in Starfleet, but the Academy is the most prestigious of the group. SFA graduate are often the best-of-the-best.
Davy Jones
"Frightened? My dear, you are looking at a man who has laughed in the face of death, sneered at doom, and chuckled at catastrophe! I was petrified."
-- The Wizard of Oz