Once again, avoid the objective arrow until you have looted the place completely, that is having all the collectibles in hand. The chapter stays peaceful until Booker tries to operate the gondola for the aerodrome, at which point hostiles will start appearing just about everywhere.
Check the metal gate next to the Tesla coil and watch the device burn out. Turn left down the hallway from this spot to find a door with a lock that can be picked. Grab some lockpicks on the floor nearby and have Elizabeth unlock the room for you. Take the Voxophone from the locker in the room full of Carbines. Go ahead and take one rifle for keeps if you like.
The safe here as with most safes in general only has money in it but requires 5 lockpicks to open, so you'll want to save your lockpicks for use on doors. A Health Infusion phial is also being kept in this office by the way. Now before sending Booker to lift the metal gate in the Welcome Center, check the room housing a scale model of Soldier's Field to find a kinetoscope by the wall.
Continue to the boardwalk, enter Dimwit & Duke's Ice Cream Shop and snag the Voxophone off the table. A kinetoscope can also be found by the railing outside the ice cream shop.
Next, take the place in some more while keeping an eye out for a shop called Founder's Books. Check inside for another Voxophone on some steps behind the cashier. Head for the gondola, pull the lever there and watch the coil burn out. Hostiles are now alert to Booker's presence so expect resistance as you head for the marked elevator. Use the objective arrow if you need directions.