Underground Living?

In contemplating the solar storms and political unrest that could easily lead to nuclear war, it has occurred to me that it might be a good idea to check out your local caverns.
My understanding is that we need to be 3 miles underground for the worst of the predicted solar flares. I am unsure how far down we would need to go to avoid radiation sickness from a bomb.
My only working knowledge of caves/ caverns are the 2 small caverns in Put-in-Bay, OH. That simply wasn't enough knowledge, so I was really excited to do an overnight trip with Cub Scouts in Blue Springs Caverns in Indiana!
Now Blue Springs is not 3 miles underground, but it gave Matt and I the chance to experience sleeping in a cavern. It was so cool and absolutely terrifying at the same time. Just the knowledge that huge chunks of rock had broken off and fallen to create the flat ceilings gave me cause to stop and think about when the next would fall.
If you have not visited your local caverns, do try to soon. It's a great family adventure and a way to measure how prepared you really are.