You're looking for a big, pillared entrance on the south-west side of the Temple of Earth area, about half-way up.
Quest
Into the Stonecore
A World of Warcraft quest in The Stonecore. Facts and objectives from the current retail game data.
The highest voted Wowhead comments for this page. They are community notes, not TheWoWDB comments.
It's also helpful to know, that NPC is actually Inside of the Dungeon.
and just incase for those who really have trouble finding it. the entrace to this instance is outside the main area. you have to fly upwards to the south-western part of the temple and there you will see a ledge with an entrance and a summoning stone.
At a glance
Into the Stonecore is a dungeon quest for level 30-35 in The Stonecore. It rewards 1 reputation reward, 600 experience and money.
Quest facts
The client quest POI data records no map location for this quest, so no map is shown.
Check whether you have already completed this quest
in-game: /run print(C_QuestLog.IsQuestFlaggedCompleted(28866))
Description
You say that this Millhouse Manastorm and High Priestess Azil were to meet inside the Stonecore? Sounds big. We'd best get on their trail. We don't want the Twilight's Hammer pulling off something big right under our noses. Speak to Earthwarden Yrsa inside the Stonecore. She's been stationed there to make sure the Twilight's Hammer doesn't try to retake the Temple of Earth.
Getting there
Inside the dungeon: The Stonecore
Within the Temple of Earth, locked in the heart of Deepholm, lies the Stonecore. It was inside these caverns that the Twilight's Hammer toiled over Deathwing, hammering elementium plates to the Dragon Aspect's body in an attempt to hold his tormented form together.
Bosses in the Adventure Guide, in order: Corborus, Slabhide, Ozruk, High Priestess Azil.
Entrance: Temple of Earth, Deepholm at 47.8, 51.9.
Instance text, bosses and entrances are the client’s Adventure Guide data.
Community notes from Wowhead · 22 comments
Top 3 shown aboveThe comments below were written by Wowhead users. They are community notes, not TheWoWDB comments. See them in context on Wowhead.
The top 3 are shown in Top Comments above. Read all 22 on Wowhead.
Reward details
Reputation: The Earthen Ring +10
This gathering of the most powerful shaman of Azeroth seeks to maintain the balance between the world's elemental forces. Their main focus during the cataclysm has been to repair and stabilize the damage caused by Deathwing's arrival.
Reputation group: Cataclysm.
Other quests in The Stonecore that reward The Earthen Ring reputation: Followers and Leaders (+500), Twilight Documents (+500).
Item facts are the current retail client’s (ItemSparse); the specialisations for a pick-one item are the ones the Blizzard quest API lists; faction and currency text is the client’s own. Lowest listed price = the US commodity auction house now.