The Northern Cave is in the northern section of the northernmost continent (not surprisingly). It is also called the North Crater or Northern Crater. It is the last area of the game that you visit at the conclusion of the story.
There is only one real visit that you will make to the Northern Cave through the story mode of the game, but you can visit the Northern Cave and leave after obtaining all of the items. Check out the Northern Cave walkthrough section for details.
Note that there is a point of no return in the Northern Cave. The point of no return is when your team all reconnects after having split up. The team will all be standing around waiting for Cloud to say “Move Out”. Until he does, you can turn around and climb all the way back to the top.
Before you complete the story, there are a ton of side quests that you can complete, which are detailed on this page:
There are a ton of great, high-level items that you can obtain by navigating through the Northern Cave so you should head down as low as you go before moving on to the late-game side quests. Some of the items include:
Counter Materia
Elixir (x3)
Guard Source (x2)
Hero Drink (x2)
HP Absorb Materia
Imperial Guard
Luck Source
Magic Counter Materia
Magic Source (x2)
Mega All Materia
Megalixir (x2)
Mind Source (x2)
Mystile
Power Source (x2)
Remedy (x2)
Save Crystal
Shield Materia
Speed Source
Tetra Elemental
Turbo Ether (x2)
Vaccine (x2)
W-Magic Materia
X-Potion (x2)
The map below shows the location of the Northern Cave on the World Map:
