We always use the National Weather Service site. http://www.nws.noaa.gov/radar_tab.php is a place to start. They have tons of information and you can easily just click the radar closest to your location and get a map on the screen that will show the storms. You can get a forecast, plus any warnings.
Local TV stations always sensationalize weather during storm season and I determined years ago to rely on the NWS. You can get as little or more information than you need anywhere in the country. Spend some time learning the site and you will be more relaxed and know whats going on.
I live in an area with severe storms and we have learned around here to be always weather aware, take a look at forecasts before we go and see what we will run into along the way.
I find radio stations, frankly, to be useless. Most are chain owned and simply repeat some feed. The great days of a real weather guy at a local radio station are gone in most of the country, certainly gone in the non metro areas. Often they will read scripts that are hours old and can be quite misleading.