Dead Island Side Quests Walkthrough: Toy Story
You get this quest from Anne Snider in the Golden Bungalow District.
To get to her, follow the minimap towards the quest givers in the golden bungalow district. The bungalow she is located in is surrounded by Zombies trying to break in. Clear them, then go into the bungalow. You will have to break a door to get in. You will find Anne in one of the rooms there. Next to her you will also find Kim who gives you another quest, a continuous event called Nectar of Life, in which you will have to bring her bottles of water.
Anne Strider will tell you she left her Teddy Bear in Bungalow #15. Locate the Bungalow and kill the zombies around it. Go in, and watch out since you will be attacked by an infected lunatic holding a knife.
After killing all the infected, grab the Teddy Bear from the green chair and get it back to Anne to complete the quest and receive your reward.