You can make several flows, each with its own weather Thing and a notifications Thing. Each weather Thing can be set to a different location.
If you want to be notified of more than one weather condition, such as fog or rain, that can be done also. But if you are real new to this, first get your flows working with just one weather Thing in each flow, looking for a real common weather condition such as cloudy, just to see it work. Then later you can make more advanced flows.
Now if you just want to get special weather alerts, not just weather conditions, you can easily do that, just pick 'new or updated weather alert in your area', and then you can select 'all alerts'. But using 'special weather alerts' might take longer to test, you will have to wait for the extreme weather condition to occur.
Keep in mind that the weather thing's performance and response time has been very intermittent for awhile, so you might not always get your notification right away.