To turn off the city location that may get posted automatically when posting a Facebook status updates do the following:
1) Start writing a new "Update Status"
2) Then when you see the location showing at the bottom of the status box (a little place icon) hover over the city and look for an X to the right of the city.
3) Click on the X button and your statuses will no longer have the location added to them automatically. (Note: if you don't see the city or X button, when posting a status update, then you have most likely turned it off)