The mysterious dog's toy is a teal dinosaur with purple spots, usually near a Chowrap billboard visible from the dog's location. Put the toy into her bed in each zone. After all seven deliveries, return to the Gap and interact with the dog there to finish Every Dog Has Her Day.

Downtown and the first toy

Look for the dog on a rooftop southwest of the Oldest House. The first toy is on a neighboring roof, one jump away. Bring it back to the bed; completing that encounter moves the dog along her chain. IGN's opening guide shows this first location.

Routes through the other zones

ZoneWhat to look for and how to return
West IncursionDog on the sideways building northwest of the parking garage. Unlock Shift at the nearby Fault; follow the Chowrap sign toward the toy on an air-conditioning unit.
Evacuation ZoneUse Reach from the street north of the vendor/fast-travel area to the toy's roof. The dog is above the red-lit area; Shift provides a way across.
CentralFind the toy below the Chowrap sign in the laser-filled alley. Return via wooden scaffolding and the suspended platform.
The ParkThe toy is across the street, east of the dog, by a high elevator. Carry power from the southwest parking area to run the lift.
UnderpassClimb the pillars northeast of the Research Site using Reach. The toy is on the opposite ceiling; follow the red route or use Shift to reach it.
UnknownUse the temporary traffic-cone/trash-can platforms to reach the dog's island. Follow rooftops toward the sideways brick building, then Shift onto the taller white building toward the billboard.

These landmarks summarize the illustrated route in Polygon's guide; its screenshots are linked in Sources when the area's gravity makes a compass direction unclear.

You cannot grapple while carrying the toy

Reach and carrying the toy do not work together. Plan a walking, jumping or Shift route back before picking it up. In Central, use the scaffolding instead of trying to repeat the grapple approach. In the Underpass, the guide drops the toy near the dog from the opposite surface, then uses Reach to return and places it in the bed.

The Evacuation Zone also has a short alternative: from the ramp below the dog, jump toward her bed and drop the toy during the brief opening. Shift makes the route easier to understand if you already have it.

The final interaction matters

Seven delivered toys do not by themselves close the quest. Visit the Gap, where the dog, bed and toy have appeared, and interact again. The source records the Trusted Spanner artifact as the reward, with a 15% raw-damage effect in its launch-version description. Verify the displayed item text in your own build before using that number in a later-patch setup.