Same sentiments here on Bing Weather. But to answer your question, app quality and availability would depend on your location. If you're in the USA, chances are you'll benefit from Accuweather and SkyMotion for hyperlocal and "nowcasting" accuracy. Now, if you're outside the USA try looking for an app that uses your local country's weather service and hope that it's free. Finally, if you can't find all of those above, just like me where the local government hasn't made a WindowsPhone App for the weather service yet, you could try RealTimeWeather or WeatherBug as these claim to use the nearest local microweather station near you.
Personally, I like to have weather data from local and international sources - and from different international models (accuweather, GFS, openweathermap, wunderground, weatheronline). This way, I get a "broader perspective" of the potential weather conditions. As a result, I have 11 (used to be 8) weather apps pinned to my start screen (thanks to live folders they don't take up much space). Some of them aren't free, but here are the free ones you may want to look at:
1. Real Time Weather (pinned) - no auto tracking of location, but uses local weather stations
2. Weather To-Go (pinned) - provides good forecast and precipitation toast notifications
3. Accuweather.com - (pinned) -useful for a "second opinion" on weather conditions
4. Breez - (not pinned) the only forecast.io app in the market that's free!, but has an app launch bug
5. Umbrella 8 - (not pinned) also provides toast notifications
6. (Bing) Weather - (pinned) if you want a "third opinion"
7. Rain Alarm - (pinned) unfortunately, I couldn't test it in my location
8. WeatherBug - (not pinned) uses local weather stations, but data sources are less that Real Time Weather... readings are off by a few degrees due to the geographic distance of the nearest weather station it uses based on my location
9. MoWeather - (pinned) not sure where they get their data, but it has been pretty accurate
These are all free as of the time of this posting. I chose not to pin some of them because another app that uses the same weather data is already pinned. Try them all (I hope you have enough phone space) and see which ones are suitable for your location.
Edit: Weather To-Go is not free. The rest of the listed apps are still free.
Edit again: Current pinned weather apps: Appy Weather; Prognoza; Weathr; MoWeather; Weather To-Go; Real Time Weather.