Half quest, half farm business would be the questline for the sky serpents in jade forest. It starts in Arboretum with saving eggs from the island nearby, then you can raise your new born sky serpent. To boost the rep in between the racing quests, you can farm eggs from timeless isle or the island from the quest and turn them in. If it’s not bugged even more than it became after MoP already, it’s kinda fun^^
Dont worry about the colour, you can buy all of them once you hit exalted. Not sure if the quest is even required anymore.
The faction also sells the recipes for the jewelry mounts, so you might want to consider doing it with a toon with this profession.
If you started playing MoP, you probably have the onyx serpent from Shado-Pan already, it’s the reward for their main quest-story line. They also sell for exalted the 3 panther mounts.
There are two riddle mounts in the game, ask youtube for details. It’s a hell of a travel^^
Likewise there are two riddle pets, B’aal, for which you need Uuna from Argus planet (which is a mount drop paradise! like 20 or so), to unlock the boss that drops Uuna (a non-fighting pet), you need to collect stuff first (easy, lies around in the world as soon as you have the starting item from mobs in the Antorian waste), then there’s a long worlds-travelling questline, since only the enhanced Uuna will unlock B’aal (a Diablo-style pet) and another one from Legion expansion. Good guides for this as well on youtube.
The hive mind mount cant be done alone though, look out for groups doing the questline.
In WOD there’s a boar and a wolf in frostfire as well dropping off their respective rare mobs.
If you ever feel like decorating the garrison, there’s a tree from Gorgrond to obtain that enhances the outcome of the garden (only get it after you unlocked the garden, else it tends to be buggy), a biting dino and the wolf a dying Orc (in Frostfire) that you help who then lives in your garrison. When you caress him, he follows you around for a while. Aah, the spoiled opportunities for housing in WOW…^^
In Tanaan, another faction sells a boar and a tiger cup (pet) for exalted. Also the Steamwheedle in Nagrand and the Arakkoa sell a Talbuk. Easy now to grind the rep for all of them. The garrison’s trade post offers another rep grind fest for one more mount. Fishing in the garrison’s pond can return two turtle mounts (probably only after the quest and the shack on lvl 3, not sure though if this is required).
Just thought I throw those not-only-drop things into it, since they’re partly quite entertaining (well, MoP and the riddle stuff, that is).^^