As the proprietor of the Wiz Chocobo Ranch (modest, isn't he?), it should come as no surprise that Wiz's quests all have to do with the well-being of wild Chocobos. After seeing to the prowling Behemoth, Deadeye, you'll be able to rent Chocobos and start Wiz's other side quests, which generally involve you riding to some area and rescuing some Chocobo. The rewards typically include the obligatory experience points, and occasionally some seeds that allow you to customize the color of your Chocobos.
Friends of a Feather
|Wiz Chocobo Outpost||Complete Chapter 2||1,500 EXP, Chocobo Whistle|
Complete the quest "Declaration of War" and hence Chapter 2, after which you'll automatically drive to the first outpost in Duscae - the Coernix Station - Alstor. When you stop, Prompto will bug you about visiting a local Chocobo ranch to the south, which starts this quest.
Head to the Wiz Chocobo Ranch (which is south of the Coernix Station - Alstor) to get the bad news: Wiz isn't renting out any Chocobos until an "unusually aggressive" behemoth named Deadeye has been dealt with. At this point the quest "Friends of a Feather" becomes intertwined with the hunt "A Behemoth Undertaking". Talk to Wiz again (who also acts as a Tipster) and take on this hunt, which forces you to venture into Deadeye's lair and slay him. Once that's done, this quest will end and you'll be able to ride Chocobos... and take on the rest of Wiz's quests.
Where the Wild Chocobos Are
|Wiz Chocobo Outpost||Finish "Friends of a Feather"||500 EXP, Xelphatol Apple Seeds / Doman Plum Pits / Mamook Pear Seeds|
When you can rent Chocobos and prove your loyalty to the wellbeing of your feathered friends, Wiz will start to ask you to check up on various wild Chocobos. First off is an elusive wild bird that dwells in Deadeye's lair. Return there, find the bird and "catch" it (run into it and press X/A) to get Prompto to take a picture Wiz wants.
Bird on the Brink
|Wiz Chocobo Outpost||Finish "Where the Wild Chocobos Are"||1,000 EXP|
Another day, another Chocobo Wiz wants you to look out for, but this one is sick! Egads! Make sure you have a Potion handy, then either drive the Regalia or ride a Chocobo to the Cauthess Rest Area to the south-west (you should have discovered this outpost when you gathered map intel from Wiz earlier). From there make your way south into the wilderness to find the ailing Chocobo at the quest marker. When you find it, interact with it and give it a Potion to get it back on its feet. Wiz will be pleased.
A Feathery Feast
|Wiz Chocobo Outpost||Finish "Bird on the Brink"||1,500 EXP|
After "Bird on the Brink" talk to Wiz again to pick up this quest, which tasks you with bringing him an Aegir Root. If you already have some, simply turn it over. If not they can be found in the wilderness north of Galdin Quay, in the crook of the U-shaped road. Also in the Galdin Quay area you can find another group of Aegir Roots east of Aldare's shop. Another place to find them is in the Ostium Gorge area, north-west of the Brackham Haven Campground.
Chase That Chocobo!
|Wiz Chocobo Outpost||Finish "A Feathery Feast"||2,000 EXP, Valfruit Seeds / O'Ghomoro Berry Seeds / Cieldalaes Pineapple Seeds / Han Lemon Seeds|
Talk to Wiz again and... Surprise! He's got another Chocobo rescue mission for you. This time one of the silly birds got itself attacked. Noctis to the rescue! This quest is quite a bit out of the way, however, as you'll have to travel to The Three Valleys back in Leide, where you'll find the wounded bird east of the central (western-most) valley, near a huge, collapsed bit of machinery. Examine the bird and you'll be attacked by some relatively high-level Saberclaws - meaner variants of Sabertusks. Once they've been culled, give the Chocobo a Potion so it can live to become prey another day.
Savior of the Species
|Wiz Chocobo Outpost||Finish "Chase That Chocobo!", Complete Chapter 7||2,500 EXP|
After "Chase That Chocobo!" Wiz will go silent for quite a while - until Chapter 8, in fact. Complete the obligatory quest "A Precious Source of Power", then travel over to the Wiz Chocobo Outpost to find that Wiz has another quest for you. Apparently a rare Black Chocobo is in trouble, and needs to be rescued. Make your way to The Vesperpool, more specifically to the Capitis Haven Campground.
From the Capitis Haven Campground head north-west across a road, past some large rocks and across another, more humble road until you find the egg in sight of the shore. Unfortunately some Sahagin decide they're hungry and you're forced to fight them off. Ignore the illusion of a timed struggled and dispatch the weaklings, then investigate the egg to collect it and come to the decision to take it back with you.
Return to Wiz and hand over the egg, after which he'll promise to call you later, after the egg has hatched. Complete some hunts and/or sidequests and get plenty of rest and you should get the call, after which you need merely return to the Wiz Chocobo Outpost one last time to gush over the cute little Chickabo.