On McCammon St., just north of the Hillside Police Department, go to the house in the corner and up to the porch. Notice the cage with the blue bird inside it. Free the bird for a short cutscene and a new sidequest:
Bird Cage
Set all of the birds free.
You do not have to do this quest all at once. Actually, it is advisable that you do not attempt to do this quest immediately, but rather do it throughout the game as you naturally progress to the next areas. Make sure to bookmark this walkthrough so that you can get back to it whenever you arrive at a new neighborhood.
Locations of all Bird Cages
Bird Cage #1 - Hillside
The cage near the police station in Hillside is probably the first cage you will run across and which will trigger the side quest. From Straub St, Go North to McCammon St. Then turn right, and pass the police station. Go to the porch of the house on the east end of McCammon St to find this bird cage and free the first bird. For all locations given here, the corresponding cages are marked by their number on our map.
Bird Cage #2 - Pearl Creek
In Pearl Creek, go east on Brite St until you hit its intersection with Lansdale Ave. This is near where the bank is. Look for the bird near one of the buildings in this area, a bit south of the bank.
Bird Cage #3 - Chastain Heights
Travel west on Brite St, and the street eventually curves north. Keep following the street to the edge, see the Queen Burger sign, and find the bird cage near a gate there between some trees.
Bird Cage #4 - Pleasant River
From King Ave., go east on Rice St until you hit the barricade. On the right side of the barricade, near some barrels and other trash, find the fourth bird cage and release the bird.
Bird Cage #5 - Port
Head north on King ave and cross the drawbridge. Take a left in the first turn after the bridge, and go all the way to the edge of the district and locate the fifth bird cage near the docks. This will be a pretty long hike.
Freeing them all unlocks the following trophy/achievement:
Birdman
Completed the bird cage side quest