I think that one of the first few GG's (I seem to generate a lot of them) should be used to get a Medic III, if you have an existing Medic II the exp can probably be shared over 2 units, if you don't have a Medic II it'll require the exp to all go to 1 unit (unless you're aggressive).
Medic III doubles heal rate in enemy territory (it's as fast as healing with Medic I in a friendly city) and this is exceedingly useful. What's more only one Medic III is typically needed and will never be lost, although if my military campaigns are particularly far-reaching I might get two. In any case I consider Medic III to be essential for any warmongering.
I'm quite fond of using very early GG's to settle in my capital and/or main military city, so units pop out with 5exp, this gives the luxury of lvl3 units without needing to run Vassalage or Theocracy. The attractiveness of this option may depend on how good of a Heroic Epic city I have lined up.
If I have a really nice HE city and/or are Charismatic I wont hesitate to mass settle my remaining GG's in one city, in order to pop out lvl5 units - it usually takes Westpoint to get them up to lvl5, though. Or I may run both Vassalage and Theocracy, which for charismatic gives a base exp of 7/8, a GG in any city then results in them popping out at lvl4. If you settle in a coastal city, all the better, because then you can pop out lvl4 boats - Flanking I and Nav I & II, really quite useful for Ironclads since move 4 Ironclads are very effective.
The "exp sprinkle" ability can be quite useful... I tend to ignore "Great Units" other than for the exp gained upon merging, a "Great Unit" tends to die unless you coddle it, and in that case it's not helping you win the war it's just a fancy mascot - that's what Medic III is for. Anyway getting back to merging, the exp sprinkle can be good to bring four 5exp units up to 10exp, also it's good to use the GG on a very obsolete unit like a chariot and upgrade it for free to a knight, or an elephant to cavalry... this way the free upgrade is guaranteed to be useful at least once and it's simply the smart thing to do compared with merging the GG with a modern unit.
Military Academies are I feel not effective. It's like a Forge which only works for military units, but you sacrifice a Great Person for it... I don't think I'd sacrifice a Great Person for a normal forge. Also it's useful in precisely the same cities as settling - those cities spending all their time pumping out units, and in my opinion settling is stronger, quality over quantity - lower unit upkeeps, you get Rep science and Sistineís culture too from settled GG's. But still, if I generate a lot of GG's I might create one or two military academies in unusually high hammer cities (especially if I have no marble for Heroic Epic).