Not a guide 
; I ain't helping with where they are in a route; I'm just showing all of the ones I find; I'm missing a lot of the Inazuma ones for sure
I can't get the runaway cats tho _(:3」∠)_ they're too quick; there's a Northland cat on Asase Shrine and a Jade-Eyed cat in Inazuma city; I've also already done the Serai Island feeding cat achievement... 
That one is a gray snow cat
Living Beings [Wildlife] page
Northland Hound
Mondstadt
You haven't seen this dog in some time, so I used a picture from an old post I made
The dog's being moved by Huffman currently
Forest-Paw
Mondstadt
Liyue
Inazuma
Shiba
Liyue
You can feed this Shiba
Were there two more at another bridge? 
Inazuma
Black-Basset Hound
Liyue
Am I missing one from Inazuma? 
I feel like I am...
Sapphire Cat
I'm missing 6 other Sapphire cats... Hmm 
or that's at least what the Tevyat Interactive Map says, I didn't check whether it's true or not 
Jade-Eyed Cat
Liyue
Inazuma
This one follows you
Behind breakable rock
Gray Snow Cat
Mondstadt
You can find this cat sometimes at the bridge above Hertha and the reputation board
Inazuma
You can feed the one in the back (only unlockable with Neko's world quests)
Behind breakable rock
Northland Cat
Mondstadt
Liyue
Inazuma
You can feed this one (w/ Neko's world quests)
Tiger-Striped Cat
Liyue
Inazuma
Sheriff Cat
Mondstadt
Liyue
Inazuma
You can feed this one (only after Neko's world quests)
Black Cat
N/A??? 
There are no black cats that aren't special in some way
You can first encounter it through Prince, Margaret's black cat, in Jean's story quest
All special pets will now be listed below
Special Pets 
Strong
Meet Strong, who puts fear in men's hearts with their barks and woof woofs
Pika
Meet Pika, a Shiba who is confused while these two people bicker about plays, all the while wagging their cute tail
Neko
Meet Neko, the Provisional Head Priestess of the Asase Shrine, who waits for Himeko to come back and maintains the shrine
You'll meet her during the Serai Stormchasers world quest
Taroumaru
Meet Taroumaru, who manages the Komore Teahouse, a place belonging to the Kamisato clan
He's also Thoma's best friend 
I'll be honest, I forgot his name, but I call him Ninja Dog
You can't meet him anymore, but his story's a sad one
That's all of the pets I found and remember so far~
See y'all and byebyes 
