The Right Stuff

This is a reference to the classic movie The Right Stuff about the space program.

I've decided to compile useful information from both comments found on this page and wowwiki and reply to the original comment which contains dated information.

Alliance:
Reputation Factions that apply a discount and where to receive the discount For Artisan Riding Skill (OP by ceciliafy below);

1. 
   
2. Stormwind Reputation - Hargen Bronzewing at Honor Hold, Hellfire Peninsula by the stables behind the <Stable Master>
3. 
   
4. Valiance Expedition Reputation - Maigra Keenfeather at Valiance Keep, Borean Tundra right next to the flight master
5. 
   

Artisan Mount Vendor Information;
Reputation Factions that apply a discount and where to receive the discount for Swift Gryphon Mounts

1. 
   
2. Honor Hold Reputation - Grunda Bronzewing at Honor Hold, Hellfire Peninsula inside the stables towards the back sitting on a Gryphon
3. 
   
4. Valiance Expedition Reputation - Durgan Thunderbeak in Valiance Keep, Borean Tundra just to the left of Maigra Keenfeather if facing her, also siting on a Gryphon
5. 
   

Horde:
Reputation Factions that apply a discount and where to receive the discount for Artisan Riding Skill (OP by blackjack90631 below);

1. 
   
2. Orgrimmar Reputation -Wind Rider Jahubo at Thrallmar, Hellfire Peninsula in the Southern part of Thrallmar behind the <Stable Master>
3. 
   
4. Warsong Offensive Reputation - Wind Rider Sabamba at Warsong Hold, Borean Tundra on the roof of Warsong Hold opposite side of the Flight Path
5. 
   

Artisan Mount Vendor Information;
Reputation Factions that apply a discount and where to receive the discount for Swift Wind Rider Mounts

1. 
   
2. Thrallmar Reputation - Bana Wildmane at Thrallmar, Hellfire Peninsula in the Southern part of Thrallmar right beside Wind Rider Jahubo (Bana will walk back and forth to a stabled Wind Rider every so often)
3. 
   
4. Warsong Offensive Reputation - Tohfo Skyhoof at Warsong Hold, Borean Tundra on the roof of Warsong Hold standing right beside Wind Rider Sabamba to the left if facing her.
5. 
   

Reputation Prices for Artisan Riding Skill are as follows: (OP by Blackjack90631 below)

Nuetral - 5000 gold
Friendly - 4750 gold
Honored - 4500 gold
Revered - 4250 gold
Exalted - 4000 gold

Reputation Prices for Swift Gryphons/Swift Wind Riders are as follows:

Nuetral - 100 gold
Friendly - 95 gold
Honored - 90 gold
Revered - 85 gold
Exalted - 80 gold

To the best of my knowledge, no other Trainers/Mount vendors will give a faction based discount.

Costs 5000 gold for the skill, 200 gold for the mount itself (If you're buying a wyvern / Gryphon), no rep discounts. Purchased in Shadowmoon Valley:

Alliance trainer:
http://www.wowhead.com/?npc=20511#.

Horde Trainer:
http://www.wowhead.com/?npc=20500