The Cosmo Canyon can be found in the southwest section of the western continent. It is the town that Red XIII is from and it is one of the central locations to the game’s plot. During the story mode there are two occasions which require you to visit the Cosmo Canyon. There are also two optional times that you can return to pick up items later in the game.
The first visit to Cosmo Canyon comes after the team makes their escape from Corel Prison and potentially after they visit the optional area of Gongaga. The Buggy that you receive when leaving the Corel Prison will break down when you get close to Cosmo Canyon.
The second visit to Cosmo Canyon takes place on Disc 2 after you have retrieved some or all of the Huge Materia. The team will return to speak to Bugenhagen and determine what they should do next.
The third and fourth visits are optional visits where you can return to Cosmo Canyon to pick up items. You can return any time after Meteor has been summoned which occurs after the events at the Whirlwind Maze. The entrance to one of the back sections of a shop opens up and you can obtain an 
Elixir, a Magic Source and a 
Full Cure Materia.
You can also return on Disc 3 to obtain Red XIII’s Ultimate Weapon, 
Limited Moon, during your final interaction with Bugenhagen. Check out the Cosmo Canyon side quest section for additional details:
There are a number of shops with items, weapons and armor that you can purchase in Cosmo Canyon:
The map below shows the location of the Cosmo Canyon on the World Map:
Butterfly Edge
Tiger Fang
Heavy Vulcan
Prism Staff
Pinwheel
Green M-phone
Silver Armlet
MP Plus Materia