Important NPCs are usually found in or around towns, although they can be found in the wild as well. There are three different types of important NPCs: Support, Main Questline, and Hidden/Sidequest NPCs.
The most notable Support NPC is Torkoal Stu, who is usually used as the save point. He can be found in every town and in the wilderness. If you give him an Afro Pick, he can heal your equipped team (up to 4 units). If you give him a Legendary Afro Pick, he can instead heal every unit you have unlocked. The merits and benefits of each option depend on the player's preferred playstyle.
The most common (lol) Support NPC is KamenAeons, who resides in each town or city simultaneously. He is usually found within the same residence as Stu, and his house often has a red cross outside of it.
Main Questline NPCs include King Talon, who resides in the Castle at UPN HQ. He gives a ton of quests, most of which I am too lazy to list out here.
DaveTheFishGuy is a Side Quest NPC, who will task you with fishing quests and equip you with a fishing rod. The fishing route is a popular strategy for early game leveling as it yields gear, loot, and massive amounts of experience. The benefits to completing Dave's sidequests include upgrading your fishing rod.