I'll be marking the Drake spawn on the map with a green dragon emblem because Drakes are green and I think it's a neat design.

Drakes take around 7 days to respawn. It seems to me that Drakes only respawn one per section of the map. This number does not include "Monster Culling" Drakes listed below. That means one Drake for Vermund, one Drake for Battahl, and one Drake for The Volcanic region.

It also seems that while the Lesser Dragon has been spawned, Drakes will stop respawning. So if you are visiting all of these locations and finding that there are none spawning you probably have a Lesser Dragon at Melve Village or at Dragonsbreath Tower. Bonus points if you kill it before it escapes from Melve. I have some advice on preventing escapes in the next section.

These are the locations of Drakes which spawn as an event. They will spawn seemingly at random at these two locations. You have to hurry if you want to kill these two because they will begin to run once two conditions are met.
1. They have only 4 health bars remaining. (that means 3 dots above the current bar)
2. They are not enraged.

To ensure these drakes don't escape, I like to leave their wings undamaged so I can get two emergency flinches on them in the clutch. If they're flying, they'll enter the knockdown state and you can deal some massive damage to either enrage them or kill them outright.

It's also worth mentioning that one can spawn at the north gate of Vernworth although I wouldn't bank on this happening. It's not a super common event and it's just as likely to be an ogre or cyclops or even a wave of saurians, wolves, or goblins at the other gate.

This guy is special because they only spawn the one time. Another fun fact about this one is that it doesn't count against the one Drake limit.
Once you kill them, they will not respawn. There's also a cyclops here doing its best.

These are the easiest two Drakes to farm because there is so little traveling between the two locations. I usually start from Harve and venture to the Drake to the north of this image, then if it isn't there I go straight south through the cave, kill the Chimera and then walk out the water where a saurian usually spawns. There is a narrow pathway that even pawns can traverse. Then it's a straight shot to the second spawn.

These guys all follow the same rules as the Drakes in Vermund. There can be only one. So I usually only hit this route if I'm desperate. I'd recommend placing a portcrystal at Dragonsbreath tower and using the pulley-cart-network to get around to the others setting out from Bakbattahl. Finding these guys can be a huge pain. But on the plus side, once you've found them you'll have spent so long hunting that the other ones will have respawned!

Correction: Actually, the northern-most drake here is a special-event Drake like the other Monster Culling Drakes.

This is the second easiest Drake to farm because it eliminates the search. It doesn't compete for spawns with any other locations. However I have also seen it up the cliff to the east of its spawn a little ways. My only theory there is that it picks a fight with a roaming pawn.

The challenge to this Drake is that there are three Wargs which will spawn by it and if you're like me you're going to want to farm those too. So you'll have to place a portcrystal there or if you're like me you'll just use the one you already have at the encampment and make a dead sprint there, wasting precious harspud roborants and pulling every enemy you pass along the way into the fight and enjoy the absolute chaos that ensues while you fight 3 Wargs, a Drake, 6 Magma Scales, and like 3 Snow Harpies all at once while the slime you passed on the way laments its existence (as we all do).