There is much you can and _have_ to do in Lake Hylia, for example, there are a few Pieces of Heart to be earnt, and also there's the Fishing mini-game, by far the most popular.

Also, once you have visited King Zora as a child, come here and where all the pillars are, near the lone pillar away from all the others is a bottle you must have the Silver Scale in order to get this bottle (you can't dive deep enough without it). Once you have it, go back to see King Zora

Also, one of the most important things you need to do is to go talk to the scarecrows, one will ask you to play a song for him, and it must be: