The Perfect Drink
Misae Suma Shrine is located in the southern area of the desert, southwest of Gerudo Town. So you will probably be frustrated to find out that when you finally get there, a Gerudo has passed out right on top of the activation pedestal. Being too polite to simply push her off, we will have to complete this Shrine Quest to find her a Noble Pursuit, a drink that she desires.
Return to Gerudo Town and go to the outer part of the city to find what is basically the city bar. You're apparently underage but if you tell the bartender, Furosa, about Pokki, the Gerudo at the Shrine, she will help you out. In order to craft a Noble Pursuit, she needs ice, and that is a bit of a snag in a desert like this. Thankfully there is a place to the north where the Gerudo store their ice.
Go to the area specified on your Sheikah Slate. It is around some ancient columns and ruins. Be sure to eliminate every enemy you see to make things easier on the way back. You will have to arrive during the day or else Anchi, the Gerudo who mans the Icehouse, won't be available.
Speak with Anchi and she will give you a giant block of ice. You only have to carry it to the entrance of the ruins and then Furosa will pick it up and finish the task. There's one catch though...it's daytime. And that means the ice will progressively melt.
To make things worse, new enemies have spawned all over the ruins and taking a hit means losing your precious ice. The way to navigate the ruins is to stick to the shadows. Your ice will remain intact so long as you leave it in shadow. Then wipe out the enemies. Beware the sun's movement as the day progresses!
Toddle your little legs as fast as you can to the entrance where Furosa will take the ice cube back to her bar. Now you will have to go back to the Misae Suma Shrine the long way since you cannot fast travel there yet.
Tell Pokki that Noble Pursuits await her back at Gerudo Town and she will miraculously revive, ready to run off into the sunset. The Shrine Quest will be complete and now you can finally activate the Misae Suma Shrine.