From Zelda Legends Wiki
A High tower made of wood connected to Outset Island on the Northeastern shore. There Aryll spends most of her time with the gulls.
Link obtains the Telescope as a Birthday gift from his dear sister here, but only to borrow for a day. But situations occur and Link doesn't get a chance to return it so he takes it on his journey.
There is a small platform with ladders at the start of the lookout. No wonder why Aryll is there at a hot day, when you can also swim in there!