If you’re looking to complete the Paying Respects side quest, you will be required to obtain the Graveyard Key.
Thankfully, obtaining the Graveyard Key is relatively simple, as all you will need to do is pay a visit to Moggie, who runs the Moogle Emporium in the Children’s Secret Hideout in Chapter 8 – Budding Bodyguard.
Unfortunately, this key cannot be purchased with Gil and will instead cost you 1 Moogle Medal. If you’ve completed the Kids on Patrol and Verified Hero side quests, you’ll be able to play the Whack-a-Box mini game to earn a Moogle Medal each time you play.
Once you have obtained the Graveyard Key you will now be able to unlock the gates to the Public Cemetery that is located in the Nuts and Bolts Hill area.