Alliance
You can find a jewelcrafting trainer in all Alliance capital cities. Like all profession trainers, they are located in each city's crafting area. If you can't locate a jewelcrafting trainer in a capital city, ask a guard for directions; doing so will mark the trainer's location on your map. Alliance-friendly jewelcrafting trainers are also located in the lowest level zones of each expansion's content. Tatiana, the jewelcrafting trainer in Hellfire Peninsula, is located in the inn in Honor Hold, while Ounhulo, in Howling Fjord, can be found in the crafting area, near the flight master. Alestos, in Borean Tundra, is located in Valiance Keep, outside of the keep itself on the left side. An additional jewelcrafting trainer can be found in Dustwallow Marsh, on the second floor of the inn in Theramore Isle.
Horde
You can find a jewelcrafting trainer in all Horde capital cities, as well as on the main floor of the inn in Falconwing Square, in Eversong Woods. If you can't find the location of the jewelcrafting trainer in a capital city, ask a guard for directions; this will mark the trainer's location on your map. Horde-friendly jewelcrafting trainers are also located in the lowest level zones of each expansion's content. Kalaen, the jewelcrafting trainer in Hellfire Peninsula, is located in Thrallmar, while Carter Tiffens, in Howling Fjord, can be found in Vengeance Landing. Goba'li, in Borean Tundra, is located in Warsong Hold, immediately underneath the place where the zeppelin docks.
Neutral
Neutral jewelcrafting trainers can be found in both Shattrath and Dalaran. Timothy Jones, the Dalaran jewelcrafting trainer, is located in the Magus Commerce Exchange; there are multiple jewelcrafting trainers in Shattrath, in both the Aldor and the Scryer Tiers. Two additional neutral jewelcrafting trainers exist. Oluros, in the Icecrown zone, is found in the Argent Tournament area, while Jazdalaad, in the Netherstorm zone, is located in the Stormspire.
Profession Trainers
The town in each race's starting zone contains a profession trainer, a special type of trainer that can teach every single profession in the game. These trainers were introduced in the "Cataclysm" expansion in order to make it easier for new players to learn a profession. Because of this, these trainers only teach the very first rank of each profession and a handful of patterns; for further training, you will need to speak with a profession-specific trainer.
Considerations
All jewelcrafting trainers teach the same recipes and will train you regardless of your current skill. If you are learning the profession for the first time or simply want to check whether you have access to any new recipes yet, you should simply head to whichever trainer is the closest to you. If, on the other hand, you are trying to level the profession quickly, consider traveling to a trainer located in one of your faction's capital cities, in Shattrath or in Dalaran, in order to have easy access to the auction house in case you need to purchase additional materials.