As soon as Booker is back on his feet, head to the far end of the beach towards the back, where a red and white striped wagon is parked. Look under the wagon to find a Voxophone. Next, look around the beach for a maintenance building that you can step into. You'll find a kinetoscope in the hallway of that building. Now, back to finding Elizabeth. She's dancing with the musicians on the dock; talk to her to grab her attention and get a move on. Also, you will want to dig around for as many health items as you can to get your life gauge up to decent levels.
Follow Elizabeth into the souvenir shop, looting it of anything you can find before heading up to the Boardwalk. There, you'll run into Lutece again. She'll ask you to pick between a cage and a bird this time. Feel free to choose whichever as your choice won't really affect anything in the game.
After Elizabeth picks the lock for the door leading to the office, loot the place and exit through the other door to a corridor. Follow this one all the way to the end, entering a storage room just past the vending machine. There is a Voxophone in the basket here along with a Gear on the table. Return to the hallway and take the passage indicated by the objective arrow, where you'll see some familiar faces. If you decided to threw the ball at Jeremiah Fink way back in Raffle Square. the grateful couple will provide you a free Vampire's Embrace Gear (Melee kills give health).
Go into the amusement center via the door ahead. Three kinetoscopes from the previous chapters are here just in case you didn't view them before. An don't forget to pick up a Voxophone from the really pristine men's rest room. Back at the corridor just past the pristine rest room is another kinetoscope. Moving on outside the amusement center, you can hold the ticket master up at gun point for some cash or demand for your tickets. Your cover will be blown either way.
Kill every enemy. Some of them carry Shotguns which pack a devastating punch at close range. Use them in the fight when you can in conjunction with your Machine Gun. Once the room is clear, before you continue past the ticket station, visit the office opposite of where the objective arrow is telling you to go. You'll find a Voxophone on the desk inside. Next, enter the ticket station from a passage in the hallway to retrieve a Health Infusion phial from somewhere in the room.
Back at the hallway once again, head straight up past the white double doors from the ticket station. Head down to the basement and search the back rooms for a Voxophone. Follow the objective arrow to the gondola and help Elizabeth with the lever. After getting off the trolley, climb to the top of the area to reach an observation deck with a telescope that you can use. Leave the area now.