Lost Mail

The quest starts with a dropped [item=134859] on the ground by a mailbox in Dalaran. Respawns approx every 2 hours.
This [item=134859] is also BoE and a copy is mailed to you upon completion of the quest, so you can give it to a friend.

- First you'll deliver it to Madam Goya in the Underbelly Lost Mail.
- From there you'll receive a mail from the Postmaster summoning you to the Dalaran Mailroom.
This room, accessible by the pet cemetery, is crammed with elementals, junk mail, even a Pepe overseer!

- You'll then sort 9 pieces of flying mail.
- That turns into A Huge Package: you will deliver 1362 Solid Stone.
(this is a throwback to The Bank of Vernal in Utah, USA)
- In Priority Delivery, someone has forgotten to loot [item=135463] and you must return it to them.
You will have to fight with ethereals trying to ninja-loot it.
- You'll then head to the Steam Pools in Feralas and find [npc=52562].
- He already has Invincible and demands you sell the duplicate to [npc=51735] in Service with a Smile.
- After returning, he then asks you to visit his SparklePony's grave in Due Reward.
- When you reach the grave, you learn that Twinkles' favorite toy was [item=45693].
- Yay for the minigame part of the questline: The Mail Must Flow:
You are asked to sort 15 letters correctly in a minute.
City and zone names will flash on the screen, and you must click on the proper mailbox for each continent.
Completing this finishes the main Postmaster questline and awards The Total Package achievement!

- You now have access to the advanced minigame, where you must sort 30 incomplete letters in a minute.
Completing this rewards the Priority Mail achievement, the [title=521] title, and [item=156721] battle pet.
[item=156833] toy is also now in your mailbox as well!

[item=156721] teaches the [npc=132366] Battle Pet.

Abilities:
[pet-ability=2013] [pet-ability=2010] [pet-ability=2012]
[pet-ability=2009] [pet-ability=2023] [pet-ability=2011]

(since this information is missing from every guide found so far)

Coordinates for "Pet Cemetary" is in Dalaran

/way 33.23, 33.81

You should see a pipe sticking out of the ground [object=247848] which you can interact with. Clicking the pipe will bring you to the Mail Room.

After playing more rounds than I care to remember, I've not seen any locations that aren't on this list for about an hour now. This is by no means a definitive list but I will check back for comments and update any new locations found.

Aerie Peak - Eastern Kingdoms
Allerian Stronghold - Outland
Altar of Sha'tar - Outland
Area 52 - Outland
Astranaar - Kalimdor
Azurewing Repose - Broken Isles
Booty Bay - Eastern Kingdoms
Bradensbrook - Broken Isles
Brill - Eastern Kingdoms
Camp Oneqwah - Northrend
Cenarion Refuge - Outland
Conquest hold - Northrend
Cosmowrench - Outland
Dawn's Blossom - Pandaria
Deliverance Point - Broken Isles
Everlook - Kalimdor
Feathermoon Stronghold - Kalimdor
Frosthold - Northrend
Gadgetzan - Kalimdor
Garadar - Outland
Goldshire - Eastern Kingdoms
Greywatch - Broken Isles
Halfhill - Pandaria
Honor Hold - Outland
Kamagua - Northrend
Kharanos - Eastern Kingdoms
Klaxxi'vess - Pandaria
Lion's Landing - Pandaria
Longying Outpost - Pandaria
Lor'danel - Kalimdor

Lorlathil - Broken Isles
Menethil Harbor - Eastern Kingdoms
Meredil - Broken Isles
Moa'Kai Harbour - Northrend
Nessingwary Base Camp - Northrend
Nighthaven - Kalimdor
Nordrassil - Kalimdor
One Keg - Pandaria
Ramkahen - Kalimdor
Sentinel Hill - Eastern Kingdoms
Shackle's Den - Broken Isles
Skyhorn - Broken Isles
Soggy's Gamble - Pandaria
Stonard - Eastern Kingdoms
Sylvanaar - Outland
Tarren Mill - Eastern Kingdoms
The Argent Stand - Northrend
The Crossroads - Kalimdor
Thrallmar - Outland
Thunder Cleft - Pandaria
Thunder Totem - Broken Isles
Tian Monastery - Pandaria
Tranquillen - Eastern Kingdoms
Valdisdall - Broken Isles
Valiance keep - Northrend
Warsong Hold Northrend
Whisperwind Grove - Kalimdor
Wyrmrest Temple - Northrend
Zabra'jin - Outland
Zouchin Village - Pandaria