Battle Pet Tamers: Outland Locations

There are four Master Pet Tamers and one Grand Master Pet Tamer in Outland and they're located all over the map across the entire continent (or planet, to be precise). The easiest way to get to the first tamer in the sequence, Nicki Tinytech, is probably through the Dark Portal that goes from the Blasted Lands on Azeroth to Hellfire Peninsula in Outland. For level 90 players with access to the Horde and Alliance capital cities on Pandaria, porting through to Shattrath City is probably the way to go.

Nicki Tinytech
Nicki is a tiny gnome who stands on the "Path of Glory" and is on the eastern side of Hellfire Peninsula:

Nicki Tinytech's location in Hellfire Peninsula

Ras'an
Sporregar resident Ras'an, the battle pet tamer in Zangermarsh is located within Sporregar on the western side of Zangermarsh:

Narrok
Orc Narrok is located in Nagrand and can be found on a road, under a tree right near the "Ring of Trials," which is just south of the Horde town of Garadar:

Morulu the Elder
Morulu lives in Shattrath and is on the south side of the city at the bottom of the Scryer's Tier where he hangs out with his tiny crocs:

Bloodknight Antari
Grand Master Antari is in Shadowmoon Valley and upon flying into the zone from the western side, you'll see him standing on a road just to the east of Legion Hold: