Ironforge is structurally a giant circle of sections, it also contains several "depth" levels (at least eight, though they are not accessible in game). The accessible portions of Ironforge appear to be located on the 5th level, the "fifth depth" of the city.
The Commons (just beyond the gates)
Gates of Ironforge (the entrance to the city)
Vault of Ironforge (the Ironforge bank)
The Great Forge (in the very molten heart of the city)
The High Seat (King Magni's throne room)
The Mystic Ward (north from the Commons)
Hall of Mysteries (Mage/Paladin/Priest guild)
The Military Ward (east from the Commons)
Hall of Arms (Hunter/Warrior guild)
The Forlorn Cavern (between the Mystic Ward and the Hall of Explorers)
Hall of Explorers (beyond the Great Forge)
The Library (quest base)
Tinker Town (between the Military Ward and the Hall of Explorers)
Deeprun Tram (accessible from the Tinker Town)
Hall of Thanes (Old Ironforge) (left door by throne room entrance, not yet accessible)
The Market - The market is located in the seventh level of Ironforge. (not accessible in game)
Hotel District - It is the district apparently in the seventh level of Ironforge, containing lodging for visitors to Ironforge. (not accessible in game.)
Sixth Depth - The sixth level of city of Ironforge, just above the hotel and market districts. Not accessible in-game.
Eighth Depth - The eighth level of the city of Ironforge, just below the hotel and market districts. Not accessible in-game.
It can be assumed that the fourth through first depths lie above the fifth depth, and lead to the surface of Ironforge mountain and likely lead to the exit leading to the Dun Morogh airfield.