In a nod to one of the side quests in Breath of the Wild that had players collecting 10 Luminous Stones to repair Zora's Domain, Tears of the Kingdom continues the reconstruction of the primary Zora residence in Hyrule in a similar vein.
Players need to talk to Ledo again to find a curious Blue Stone that is apparently crucial for making Zora architecture in order to repair the statue of the late Princess Mipha, the beloved daughter of the king, Dorephan.
Where To Start The Blue Stone Quest
To begin The Blue Stone side quest, you will first need to complete the "Sidon of the Zora" questline and clear the Water Temple. Once Zora's Domain is free of muddy water, head over to the East Reservoir Lake and talk to Ledo. He is standing on the dam's edge, looking at the lake. Talk to him to begin the quest.
Where To Find Blue Stones
Ledo will tell you that he needs a Blue Stone to repair Mipha's Court and that he's discovered a cave full of Blue Stones. He'll show you the location of the cave in a short cutscene.
Your task is to head inside the cave and carry one piece of Blue Stone back to Ledo. To do this, you will need a lake-worthy boat. Luckily, there are some Zonai Fans, a Steering Wheel, and a couple of wooden planks to the left of where Ledo is standing.
These Zonai devices are easy to miss. They're hidden behind a large protruding black rock that's adjacent to the bridge Ledo is standing on. You can also craft your own Zonai vehicle to make the journey to the cave, but this way, you don't waste Zonaite unnecessarily. Combine the parts to form a power boat like the one shown below.
Use the boat to sail inside the cave that Ledo pointed out to you. After covering some distance, you'll see a place to beach your boat. Stop here and look straight ahead to find five or so Blue Stones stacked next to each other in a small cavern. Lift one Blue Stone up using Ultrahand and attach it to your boat.
There is a Bubbul Frog in a chamber to the left, hidden by some vines. Collect the Bubbul Gem on your way out.
Drive out of the cave with the Blue Stone attached to your vehicle and head back to Ledo.
Use Ultrahand to detach the stone and place it in front of Ledo, and a short cutscene will play with Ledo acknowledging your contribution and rewarding you with the Zora Fabric, a new fabric for your paraglider.
With this, The Blue Stone Side Quest will be marked complete.