Upon acquiring the chance to freely roam Beach City, you can talk to Kofi Pizza, the owner of Fish Stew Pizza. He'll tell you to help out his deliveries since this is all your fault and to talk to his daughter Kiki beside him. She'll send you to a handful of places to deliver pizza.
1) Suitcase Sam
Ol' Sam can be found on one of the roads in the back part of Beach City, near Ronaldo and Jenny.
2) Onion
Onion is the "mysterious shopkeeper" you can start finding out in the wild as early as the Beach City Woods. Chances are highly likely that you don't have to go to a specific location to give it to him.
3) Amethyst
For me, I took the pizza and then made sure I had Amethyst in my party. This makes it to where you can talk to her with the pizza in your Key Items and give it to her this way. I'm not sure if there's a specific location or set-up you need in order to do this, but I went to Steven's house just in case (as I thought the members not in my direct party would have been chilling out there).
By returning to Kiki, she'll say there are no more deliveries, and you can talk to Kofi to finish the quest.