The Rare Coffee side quest involves hunting down coffees from around the world and returning them to a man named Morrid. You can find Morrid in his home at the base of the Observatory Mountain, which plays a key part in the early part of the story, and can be found just outside of the Village of Dali.
The first time you visit Observatory Mountain is early on Disc 1 during the visit to the Village of Dali after completing the Ice Cavern. Walk into Morrid’s House at the base of the mountain to view his miniature model of the Prima Vista. He will agree to give it to you if you collect three rare coffee beans for him; specifically you will be looking for Moccha Coffee, Kirman Coffee and Burman Coffee.
This coffee can be found at the South Gate (also known as the Bohden Arch on the game menu screen). The South Gate is located to the west of Pinnacle Rock. Search the area near the water to find the hidden coffee.
This coffee can be found in Eiko’s house in Madain Sari on Disc 2. Search the left side of the kitchen to find the coffee amongst the cooking utensils and supplies.
The last coffee can be found in the Village of Dali on Disc 3 (during the Treno section of the story). Travel back to Dali and into the Windmill and take the pathway through to the left side and into the mayor’s house. Choose to “check the room” and you will be prompted with a list of areas you can check: the Desk, Ladder, Heater or Shelf. Check the Heater to receive the Mayor’s Key and then choose to quit.
Use the Mayor’s Key to open the doorway at the back of the Windmill room near the Chocobo. This will lead you out to the Chocobo’s Pen. There is a hidden treasure chest on the right side of the screen that contains 30,000 gil. Examine the treasure chest a second time to find something hidden underneath the box - the Burman Coffee.
Travel back to Observatory Mountain to provide the three coffees to Morrid. He will reward you with the Mini-Prima Vista ship and will send it to the Tantalus Hideout in Lindblum. Search the floor near the bed to find it.