A simple script when run pops up with a libnotify notification. Assigned to a keyboard shortcut and works like a charm!

weather.py

# -*- coding: utf-8 -*-
#!/user/bin/python
from gi.repository import Notify; import json; import urllib2; import sys
reload(sys); sys.setdefaultencoding("utf-8")

city_name = "Insert City Name Here"
city_data = json.load(urllib2.urlopen("http://api.openweathermap.org/data/2.5/weather?q="+city_name))
city_temp = str(city_data['main']['temp']-273.15)
city_weather = city_data['weather'][0]['description']

Notify.init ("City: " + city_name + " " + city_weather)
Hello=Notify.Notification.new ("City: " + city_name, "Weather: " + city_weather + " - Temperature: " + city_temp +"°C","dialog-information")
Hello.show()