Blackrock Depths

Instance quests for Blackrock Depths
 * Level: 54+
 * Zone: Blackrock Mountain

The entrance to Molten Core is inside Blackrock Depths. After you clear the Room of Seven, before you enter the Lycaeum, take a right, and cross a bridge. The green portal there takes you to Molten Core.

Badlands

 * The Last Element
 * Lost Thunderbrew Recipe
 * Disharmony of Flame
 * Disharmony of Fire
 * Kill on sight: Dark Iron Dwarves
 * Kill on sight: Dark Iron Officials
 * Operation: Death to Angerforge
 * Grark Lokrub
 * Commander Gor'shack
 * The Royal Rescue

Blackrock Mountain

 * Dark Iron Legacy

You need to be a ghost in order to get this quest. The npc is inside the middle structure in blackrock mountain, suspended above the lava.

Blackrock Depths

 * The Love Potion

Burning Steppes

 * Rise of the Machines
 * The Rise of the Machines
 * Ribbly Spewspiggot
 * The Heart of the Mountain
 * Taste of Flame

Taste of Flame has two possible pre-reqs, but you only need to do one of them. The first is Kalaran the Deceiver's entire line of quests in searing gorge or simply talk to the npc who gives Taste of Flame, and tell him you accept his challenge. You fight an elite drake and loot an item off him, which allows you to the get the quest. However, only one of said item drops off the drake, so you have to repeat it to get everyone in your group to that stage.

Adapted from World of Warcraft Instances/Quest Guide by Durn  of Burning Legion