I think the best weather widget to add to a website is weather.com, but I think they ask too much question for a free service and I do not think they give time on the widget and what I do not like it open a new page, the weather.com page to give the weather result. However they allow the visitor to choose the weather for his/her location.
The second one is the weatherReport.com, this one you do not need to sign up and give your age and so on. It allows you visitor to choose the weaher for the location thaty he or she needs, but it opens in a new page. The result did not appear on your own website. Tere is no time.