Once you've landed at the gondola station you should turn around to uncover Vantage point #22 - Telescope.
There's a gondola nearby and it has a locked cabin. Ask Elizabeth for help in opening the cabin (you must have 5 lockpicks) and take a look inside. You will find a silver tab here, as well as Gear #15 - Legs.
Before you leave the gondola station you should explore the area and interact with the Dolar Bill vending machine. You can purchase 3 lockpicks and each lockpick costs 48 dollars. Once you're ready proceed to Finkton Proper.
Enter the building, turn left and search the area under the stairs in order to obtain a new lockpick.
The left corridor also contains a machine used to upgrade vigors and Vantage point #23 - Kinetoscope.
Proceed to the building's main hall and explore the office located in the middle. There are two important items here - a lockpick and Voxophone #36. You should also check the floor near the desk to find a bag filled with money.
Explore the area behind the main desk to find yet another lockpick hidden between a smaller desk and a scale.
A locked room can be found nearby. Ask Elizabeth for help in opening the lock (5 lockpicks are required for this activity). There's an Infusion #12 on a desk to the right and exploring the back area of this office will allow you to collect a Volley Gun among other things.
Walk past the people standing in front of a vending machine located in the middle of the hall and use the stairs (it doesn't matter on which side) to get to a lower floor. Locate a new locked door here. Thankfully Elizabeth can open this door without using any lockpicks.
The room on the other side of the door you've just opened is guarded by a Mechanized Patriot and a squad of policemen. Your objective is to get to a service elevator located on the ground floor. Expect reinforcements to arrive from the upper floor and fight your way to the lowest level.
Once you've defeated all hostile units you should explore the entire hall. A room located opposite the elevator contains a shotgun and a locked safe. You only need one lockpick to open this safe and it contains about 100-200 coins.
Make sure to check the trash bin located next to one of the bookstand in the middle of the hall to obtain a lockpick.
Go to the room with the elevator. There's another lockpick on one of the desks near the window.
Press a button to call the elevator. Elizabeth should approach an opened locker at this time and it's wise to take interest in it as well, because it contains Voxophone #37.
The elevator will stop half way to its destination. Pick up a phone hanging near the glass to continue your journey.
When you'll get to the ground level Flambeau will already be waiting you. Check the table seen in front of you to collect medical supplies, money, a lockpick and a new weapon - Hand Cannon. This is a revolver which holds six bullets and offers supreme firepower at a cost of low fire-rate. You should also know that finding ammunition for this gun is not easy. I recommend the Hand-Cannon to experienced shooters who like to kill their targets with single shots and never miss. Once you're ready leave the building to advance to the next chapter.