heh...interesting. You must have enabled location services when you set up the machine. You can somewhat configure it by going into System Preferences -> Security & Privacy -> Privacy, and unchecking Weather. This at least allows me to remove the only city that cannot be removed in the widget, which actually has a location icon next to it. I'm looking at this on a desktop at work so I don't know if this will specifically address your issue, but it might point you in the right direction.
One thing thats strange is that your location didn't update when you connected to the internet in your home city. Maybe this data isn't updated, and toggling it on and off will force an update with the proper city. Maybe disabling the widget and re-enabling it would force an update as well. At the very least you can disable location services for the widget and manually enter your city.