BioShock Infinite: Unlimited Money Guide

There's an area in the game called the Hall of Heroes (or the Hall of Whores, if you prefer to read it that way) in which you can get unlimited amounts of Silver Eagle currency by exploiting the vending machines.

As you know, you can use your Possession skill on vending machines to get money out of them. You can only ever use the possession skill on a vending machine once to get currency from it, but this particular area in the game allows you to use the Possession skill as many times as you want on the vending machines for unlimited money. 

Additionally, there's a salt dispenser within the Hall of Heroes that you can use to replenish your salt so you can use the Possession skill without worrying about running out of energy. 

Keep in mind that doing this will only yield 20-30 Silver Eagles per vending machine, so it might not be worth doing unless you intend on picking up all the upgrades for your guns and Vigors available to you at that point in time.