A Feline Feast - Cape Caem
First Available: Chapter 7
Other Requirements: Complete Kitty Catering
Location: Cape Caem
Rewards: 1,200 EXP & Sky Gemstone
You'll find this quest behind the lighthouse in Cape Caem if you did the Kitty Catering side quest earlier in the game. There are two different routes you can take for this quest after accepting it. First, you can listen to the quest and go speak to Monica who then sends you to a nearby fishing spot. Much like Kitty Catering this route will involve you cooking a meal for the cat.
Alternatively you can zip down to the location your car is parked when you fast travel to Cape Caem and speak with the vendor nearby the red truck (pictured below). Under Key Items you'll find the Luxury Cat Food for sale which costs a whopping 20,000 Gil! Purchase this and return to the cat to complete the quest - obviously this is the more expensive route but it's much more expedient to do it this way.
Completion of this quest will get you the Sky Gemstone which is a very rare item that's used in the A Better Circular Saw Side Quest.