Enter the Soldier's Field Welcome Center and turn left to find a locked door leading to the security room. Notice a lockpick near the door. Take this item and allow Elizabeth to use it to open the lock.
Once you're inside the office check the desk under the window to find Infusion #6. Explore the rest of the room and also take a look inside a nearby study.
The study contains a locked safe and in order to open it you're going to need 5 lockpicks so return here once you've gathered the required number of these items. One of the lockpicks can be found on a desk behind the safe. You should also inspect an opened vault located to your right - you'll find a rifle there and Voxophone #22: A Place in the World - Daisy Fitzroy.
You may now proceed to the left part of the pavilion where you'll find Minuteman's Armory vending machine. Check a wooden crate located to the right of the vending machine in order to obtain two lockpicks.
There's a model of the Soldier's Field a little further ahead. Inspect the area behind the model to unlock Vantage Point #15: Kinetoscope - A City in the Sky? Impossible!.
When you'll approach the exit from the pavilion the electricity will malfunction and the door will close. Open the door using brute force. Leave the building and enter the main area of Soldier's Field.
As soon as you've stepped through the gate turn left and walk past Duke and Dimwit's ice cream shop. You'll soon unlock Vantage Point #16: Kinetoscope - Mighty Songbird Patrols the Skies!.
There's a new Voxophone #23: I Am His Mirror - Zachary Hale Comstock on one of the tables inside the ice cream shop. If you're not looking for trouble, then I strongly suggest that you don't make any attempts to steal money from the shop's register. Each time a container turns red it means that someone is guarding it (in this case it's the person selling ice creams) and you can expect the authorities to be informed about your crime. Furthermore, you won't miss anything if you don't steal from this register and you'll be allowed to return here later on when the ice cream shop will be closed.
You may now proceed to the Founder's Book store located to the right. Check the entresol to uncover Voxophone #24: Viewing the Infinite - Rosalind Lutece.
Once you've left the book shop turn right and use the promenade to get to the Toy Soldiers store located next to the carousel. You can steal the Heater's replica if you want to, but I suggest to drop the subject, because you would have been noticed by the policeman guarding the object. Heater is a shotgun manufactured by Vox Populi and you'll have more opportunities later in the game to add it to your arsenal.
Leave the store and inspect the carousel's stairs to find another lockpick (a shining object seen on the screen above).
Descend to the promenade located beneath the carousel and turn right. Proceed to the gondola which travels to the First Lady airship. Approach the gondola's panel and pull the lever. The device will malfunction and in order to activate the gondola again you're going to need a Shock Jockey vigor.