Where to find cats
As part of the Lost Friends quest, you have to find Betty's three cats. This involves finding each of them, trying to call them, and moving on to the next chat until you've done that with all three. None of the three cats are on the map either, so you'll need to scour the slums in Section 7 to find each of the cats.
While there isn't a specific Fallen to find the cats, the first one we'll be describing here is near the building Cloud is staying in. Around this area you will see a lower area that you can descend into which is still out in the open air where a woman is screaming in an open lane. This woman will have a green quest marker above her head once you get close enough, so be sure to talk to her. She will mention that she was trying to get a cat out of there because she took one of her pastries, so head to the open path and you'll find a collection of many cats on the other side. The mission isn't over just because we've found a group, as only one of these cats is the one we need for Betty. Talk to the white cat you see and can interact with and you can move on to the next one.
The second cat is really easy to find because it is in plain sight. You've probably seen it before and haven't thought about it because it wasn't part of a quest. For this one, just head to Seventh Heaven Bar, Tifa Bar, and Barret Bar, and you'll see the cat sitting right on the porch. Again, speak with the cat and it will walk away.
The third and final cat is a little harder to find than the second. From the seventh heaven, when you turn away from the bar, you want to go down one of the paths which is right and a little to the left. As you walk this path, Tifa will talk about hearing a cat, which means you are in the right area. Once you see her talk to the last cat and you'll have the option to automatically return to Betty to complete the quest.