Since pretty much every quest in ST is part of a long-ass chain, I wanted to make this guide to list them all, and what should be the most efficient way to get them all, since you'll be flying all over Azeroth.
Quests:
- Haze of Evil: Chains off the Muigin & Larion quest in Un'Goro to collect Bloodpetal Sprouts. Then they send you to Feralas to talk to a dwarf who sends you into ST for Atal'ai Haze. I generally skip this quest as the Bloodpetals are a pain, drop rate sucks, and the quest reward is lame.
- Into the Temple of Atal'Hakkar: Long chain starts with Brohan Caskbelly in the bar in SW Dwarf Quarter. He sends you to find the Temple, after you swim up to the temple and return, he sends you to talk to a Dwarf at Aerie Peak (Hinters), they send you to talk to a drunk dwarf along the path leading from the Hinterlands to EPL. This dwarf wants you to get him the ingredients for a "Kalimdor Kocktail", which involves killing mobs in Feralas and Tanaris. Once you get him these ingredients, he sends you back to the Dwarf in SW, who finally gives you the ST quest.
- The God Hakkar: The longest chain in the ST quest line, and possibly one of the longest chains in the game. It starts around level 40 when the troll Yeh'kinya in Steamwheedle Port asks you to kill screechers in Feralas and capture their spirits. Once you've done that he'll want you to collect tablets from two minibosses in Zul'Farrak, the Hydromancer and the Martyr. Now that is done, he'll send you to the Hinterlands to get an ancient egg from the top of Jintha'alor. Once you have the egg, you'll be sent into ST to summon and kill Hakkar. The quest chain continues on after this into Lower Blackrock Spire and the Plaguelands if you keep following it. Good XP from 40-60, and some good rewards along the way.
- Into the Depths and Secret of the Circle: The second easiest quest chain, and it gives two ST quests! Marvon Rivetseeker is at Broken Pillar in Tanaris. Talk to him and he'll ask you to fetch a stone circle from his house in Ratchet. Now that there is a FP at Ratchet, this is cake. Fly there, grab it, fly back and get both these quests.
- Jammal'an the Prophet: The only non-chained ST quest. There is a troll exile on the steps of the largest temple in Shadra'Alor in the Hinterlands. Talk to him and get the quest. The rewards are pretty good too, if you wear cloth or mail.
- Class-based quest: Shortly before WoW 2.0 launched, they added a quest in ST unique to each class. An NPC near your class trainer in a capital city will send you to talk to an NPC when you are 50 (possibly earlier). Follow that chain and get an ST quest that will give you a choice of three items specially built for your class.
So now that the quest explanations are out of the way, here's what I've come up with for the most efficient way to get them all (assuming you've done the prereq quests for Yeh'kinya's chain). This guide assumes you're starting in Tanaris because most of these quests can be started immediately after ZF, and Tanaris is a good place to level at the mid-40s.
- In Tanaris, talk to Marvon and get his quest to go to Ratchet, and make sure you have the ancient egg quest from Yeh'kinya (now would be a good time to do the bloodpetal quest in Un'goro if you want to), then head to Stormwind.
- Once in SW talk to Brohann, go find the temple in the Swamp of Sorrows and return.
- Fly to the Hinterlands and get the Kocktail quest as well as the ancient egg for Yeh'kinya, on your way out, swing by Shadra'Alor and get the Prophet quest.
- Now head to Booty Bay and take the boat to Ratchet, picking up the stone circle for Marvon.
- Fly from Ratchet to Feathermoon in Feralas and collect the Ironfur and Groddoc livers. These can be acquired from mobs right next to the dwarf that Muigin and Larion sent you to talk to for the Haze quest (South of the Twin Colossals).
- Now fly to Tanaris, get the Roc Gizzards to complete the Kocktail, and give the egg to Yeh'kinya and the stone circle to Marvon.
- Head back to the Hinterlands, give the Kocktail to the dwarf there, return to Stormwind and pick up the final ST quest.
Now I haven't done anything as pedantic as make sure that this path takes the absolute least amount of time, or has the cheapest flight paths, but it does get all the quests with the minimal amount of zipping back and forth between continents. It's unfortunate that you must make two trips to the Hinterlands no matter what, since it is so far away.
However, a crafty player will notice other quests that fall nicely into this path. Marin Noggenfogger's quest chain will send a player to the Hinterlands for a mushroom. If you're willing to extend the path a bit, you can get the moonkin feather quest and the Gammerita photo quest completed at the same time (most easily accomplished if you were questing in Feralas before, and got the quest to go to Rut'theran Village for the book on Feralas, then directed to the gnome in Gadgetzan, and then to the Hinterlands, see the Tanaris/Hinterlands pattern? =) ).
I mostly wrote this for myself and my friends, since we do these instances together, and I'm a stickler for quest efficiency, and this dungeon's quests used to drive me absolutely batty by making me go back and forth between arguably two of the furthest points apart on Azeroth.