During the visit to the area with the Village of Dali, you will find another location called Observatory Mountain right next to it. Go inside the building here to meet with an old man named Morrid. Speak to him, then inspect the airship model on the left side of the house to have Morrid mention he will give it to you if you find him some rare coffees.
Missable: This side quest is missable, as if you don't finish it by the time you start the next section after Ipsen's Castle, then you will be locked out of the Observatory Mountain.
There are only three coffees to get and one of them is missable, so you have to make sure you get that one during a certain point in the story. Once you have all three of the coffees, bring them back to Morrid at the observatory. He will send the airship model to Tantalus' hideout in Lindblum.
The first coffee you can find in the game is the Moccha Coffee, which will be located at the South Gate that's east of the Chocobo's Forest. There is a branch on the right side you can walk on, so do that and search around there to find the Moccha Coffee.
You will be able to find the Kirman Coffee upon reaching the Outer Continent and gaining access to Madain Sari. Whenever you are able to go into the kitchen area of Eiko's house, you will find the Kirman Coffee in between the one table and the staircase leading down to the docks.
This is the missable coffee, as you can only grab it during the trip to Treno, when the card tournament is ongoing. Leave Treno and pass through the South Gate, heading back to the Village of Dali. Enter the windmill and then the mayor's house, where you'll find a kid sleeping. Check the desk three times, then check the stove afterwards to find the Mayor's Key. With this in hand, you can open the locked door in the windmill, leading to the chocobo pen. On the right side of this pen will be a chest, with some money inside. Check the chest a second time to uncover the Burman Coffee.