Something that I've already worked up, except for the graphics, is a gambling game, so that the player can lose all of her money.
(Of course, she might be able to win some too.)
A speculation system would be even easier, b/c you could have the player buy stocks by a certain time and have updated prices at other specific times and the player could choose to turn in her stock whenever for the current value. You could have a more complicated system that reflects the City's events in the prices going up or down, too.