The power of Twitter is in the ability to quickly see what is happening in any given situation. Think about the Arab Spring; it was amazing to see what was happening in Egypt through Twitter. One way that is accomplished is through hashtags.
One of the most universal hashtags is the weather! Whatever state you are in or traveling to you can search for weather. Media, storm watchers, local people and more use the tag.
The key is to use the #YOUR TWO LETTER STATE ABBREVIATION plus WX. SO, if you are in California it is #CAWX, although growing up there your weather doesn't change enough to even justify a weather person on the news!