Talking to NPCs to find out things about the immediate area is a major part of the game.
If you do what the King says, you’ll encounter NPCs that have some early world building dialog, an easily climbed tower to start filling in the map and get the shrine sensor, four convenient shrines, one of which has the climbing bandana in it, great time to get that because you don’t have a hat at all yet so the extra armor plus the climbing speed buff is excellent to have, there’s a stable with a sidequest that teaches you how to catch horses, you’ll find Hestu along the path up to Kakariko and likely increase your inventory (or learn that koroks exist), and then in Kakariko the shrine there is a combat tutorial, there’s a fairy fountain nearby, plus Impa sets you on the main quest of the game. Having done four shrines, you can add a heart or stamina wheel sector. Pikango is here, and there are several sidequests in Kakariko to get stuck into.
Impa sends you to Hateno to get the memories sidequest going. Major location in the game with some adventuring and side questing to do, more expository dialog and world building, you get the camera and shiekah sensor, get sent back to Impa, and then you’re kicking around in Kakariko with no immediate goal. You look out one of the exits of town you haven’t taken yet and you see a wide open area with two visible shrines and a tower. Course charted, you get sucked into the Zora plot. Once that’s done, you’ll have Mipha’s Grace, an additional heart, some more armor, and then the training wheels are off and now it’s up to you to pick a direction to explore.
“I didn’t do what the NPC said and didn’t find something important the whole game” gives big “why don’t my kids ever call” energy.