The Weather Channel
There are two great sources. One is the Weather Channel, which you can get on your phone or computer as an app. The other is NOAA, which is the official weather warning station. NOAA also gives alerts. They can be accessed on your phone, computer (as an app or at their website) or on an emergency radio. The emergency radios are a great option as they can usually be charged in 3 or 4 different ways, including a crank, so you will not be without information no matter the situation. They are not terribly expensive. The NOAA app on your phone can give warnings, too. We have a couple, one more expensive one that is going to reside in our trailer and can communicate with walkie-talkies we have, and an inexpensive one (about $10) that resides in our emergency bag.
I hope this is helpful!