On my Galaxy Nexus running stock Jellybean 4.1.1 the News & Weather widget thinks I'm in Hong Kong airport, and has for the last week.
I have been to Hong Kong airport 3 times in the last month (it's a hub airport for Australasia) but never stayed there for longer than 3 hours. I'm currently in London, and have been either here or elsewhere in England for the last 7 days.
If I tap the widget and tap the refresh icon (circled-arrows) it does show the correct location until the next auto-refresh interval (I have it set for 6 hours) when it will switch back to "Chek Lap Kok Airport" in Hong Kong again.
Following the instructions in this previous question News & Weather Widget Not Updating I have deleted the widget from my home screen, done a Clear Data and Clear Cache on the News & Weather app in the applications listing, and then re-added to my home screen. This sorted it out initially, and then 6 hours later it switched back to Hong Kong again.
I have all of the Location Services in the Android settings enabled, Google Maps shows me in the correct location whether I'm outdoors (on GPS) or indoors (using network location). I leave Wifi switched on for most of the day, and this happens during the day at work when I'm using mobile data, and overnight at home when I'm connected to my wifi.