From the station, search the trash cans for loot and restock with the vending machines if you need to, before heading through the door into Monument Tower. Welcome to Monument Island achievement / trophy unlocked. This chapter's focuses mainly on exploration is pretty much combat-free. There are quite a few collectibles scattered around though. Make sure to pick up all of them as this is the only time you will visit this place.
Grab the hook above the gate to get inside the facility. At the lobby (where there is a large angel statue in the middle), turn to the left checking the lockers for a Voxophone. Just past the first set of doors is a hallway with a giant siphon machine. Proceed past the door behind it and turn toward the first passage to your left. The airtight steel door leads to an exam room that houses a Voxophone.
Go ahead and check out the other two rooms, before heading straight through another set of double doors further down the corridor. Snag the Voxophone from a desk inside, and on the floor to the right behind the desk with the Voxophone is a Health Infusion phial.
From here, continue through the level until you reach the third observation chamber that is on top of some metal stairs. There is another Voxophone on the chair next to the lever. Escape the tower with Elizabeth and you will eventually end up on Battleship Bay.