(Lots of spoilers)
This is my concept for a more immersive way of finding the stones. Rather than no quest markers, or having ALL of the quest markers, I thought it would be neat to have a fun, thiefy, in-game experience. You don’t want to be a thief with no leads – it also doesn’t make sense to have leads on every stone all at once. A good thief makes friends and those friends tell you where some nice pieces of loot can be found.

If you want, you can still find all of the stones in the traditional way, but for those who want some immersive help this was my idea:

As you begin to rebuild the reputation of the Thieves guild and progress in the main TG quest line you gain new contacts in each of the holds. If you have started No Stone Unturned and identified the first stone from Vex you start to receive courier letters from one of these contacts (similar to the letters you would get “from a friend” when uncovering words of power).

When you open the letter, it points you to one of the stones. You don’t receive another letter until you recover that particular stone and perhaps other criteria being met. You won’t receive letters from a certain hold until that hold feels the influence of the Thieves Guild (i.e. you have completed that special job and have created a network in that area).

Vex would be your first contact and would have leads for stones in The Rift (Mistveil Keep, Black Briar Manor, and Ansulvund etc.). Tonilia can sell you the one from the Dark Brotherhood if you aren’t a member and don’t feel inclined to wipe them out. If you do the quest from Dagur in Winterfell that surrounds Ranmir’s lover who went to Vex to a lead, she can also give you a note about the gem in Hob’s Fall cave.

Vekel – Get a note from Vekel after you accept the quest to get the journals about the gem in Yngvild.

Mallus sends you notes about gems in Jorrvaskr and and the Hall of the Dead. Mr. Battle Born can tip you off to the one in the Jarl’s bedroom after you have completed the special job for him.

Enthir can sell you the key to Winterhold and the Archmage’s Quarters after completing Blindsighted. He can also point you to any keeps or caves that have mages of ill repute (Fellglow Keep, Sunderstone Cave, Rannveig’s Fast). He can also send you to Wunfurth the Unliving.

Erikur can point you to the gem in the Jarl’s palace, and Gulum Ei can sell you the key to Proudspire after completing the special job in Solitude. He can also point you towards reeking cave.

Niranye can point you to the one in Clan Shatter-Shield’s house.

Endon can point you to the one in Pinewatch (if you missed it), the museum and the one in the treasury. He can send you the one out at Dead Crone watch as well.

I would be willing to write up the content for the notes. I know this is similar to other quests, but I haven't seen anything quite like it. Let me know if you think it's viable and would like to work on it. Or if it's super easy for a Noob to do, tell me how to get started. Thank you for taking the time.