ZigWeather gives you a multi-widget to show weather on your site.
You can try a few different formats in order to get the widget to show weather for your desired location:
If the widget displays "Data cannot be shown" or shows the wrong location, try a different format or a different nearby location. For example, in Malta, the API doesn't know where the town "Bugibba" is, but it is happy to take "Naxxar" which is a slightly larger town about 3km away.
The plugin gets fresh information each half hour, and whenever you change a location. However, the World Weather Online service only updates its API data every 3 to 4 hours. But hey, it's free.
More information can be found at World Weather Online.
Go to the settings page and set the "Load stylesheet" dropdown to "None" then save. You will now need to add some styles in your theme stylesheet.