I highly suggest you to try out my-weather-indicator
. It will satisfy all of your needs.
Here's a screenshot showing the weather in Amsterdam:
Installation instructions
sudo add-apt-repository ppa:atareao/atareao
sudo apt-get update
sudo apt-get install my-weather-indicator
It kind of has a huge dropdown menu once you right-click it that shows you the detailed info, but that's the only disadvantage of it I can think of.