If you are technogeeky and want to really get into it, the thing to use is not a web site, but a program that downloads the NWS radar data and displays it in various form without waiting for the web site to update, to change from one view to another, to animate, zoom to your location, etc.
These are the radar tools to figure out "where is the tornado/storm and is it going to hit my house?" You need some geek cred to really understand and use them well.
Grlevelx is the primo program in several versions. It's a commercial web site, so you'll have to Google it yourself.
Grlevel3 sells for $80 and is easiest to use. There is a 21 day trial version.
Grlevel2 has better and and more detailed data, but the "level 2" data is a little more complicated to acquire. Many GR2 users pay for access to the data from a commercial site.
On Android, there is Pykl3, which has similar advantages for watching the radar, but it just can't compare to grlevelx in terms of usability due to screen size and other limitiations.
The free, online NWS (National Weather Service) site with similar radar data is: http://www.srh.noaa.gov/ridge2/ridgenew2/
The free NWS site displays a lot less data than the "offline" tools like Grlevel3. It doesn't display some of the newer more techno dual polariziation radar products. It's also much slower, especially during weather events to scroll or animate due to requiring on the web server, not your computer to display stuff.