It's through preparation. It allows you to be ready and yet live your life outside of consent fear. Its not expensive and it provides for a piece of mind.
*Disclaimer* I am not an expert. I just have a bunch of low level training and like basic research. These should only be considered suggestions and not recommendations in anyway. Further if I miss something let me know and I'll add it in.
There are two basic kinds of attacks. They are conventional (bomb, armed terrorists) and unconventional (Nuclear, Biological). You really can think of it this way: conventional your radius of escape is relatively small and the duration of the danger is relatively short and unconventional, your radius of escape is long and the duration can be very long. Further, if it is biological, contact with your fellow survivors can put you at further risk.
What you need. I will start with unconventional terrorist attack. I am going to assume that you have escaped from the epicenter and managed to find your way to your vehicle.
1. Map. Find out your gas mileage and your gas tank capacity. Draw a radius on your map, this will be you r operational range. This is what you need to mark. Find all military bases, national guard depots (a careful internet search can reveal major fuel depots), BSL-3 and BSL-4 biological research centers, small local medical clinics, veterinary clinics, water pumping stations, food pantries , nuclear power plants and rural college campuses.
Break down: Military bases is an obvious one it can provide protection, medical, fuel, water, gear etc. But in an attack their number one priority is to remain operational so that they can provide a continuing response to the attack and its after affects. They may or may not let you in.
National guard depots-they tend to be lightly manned but chock full of useful stuff. Fuel, food, vehicles, medical supplies. They tend to be tucked away and not well known but once again a ten second internet search will provide you with the details you need. The downside is they are very lightly or if at all manned if you need help you are probably on your own.
BSL-3 and BSL-4 biological research facilities. They are the one place you can run to and be fairly assured that the Small Pox or Ebola can not get in. They will also become the epicenter of the coming response. The major problem is lack of food, water and their existing security. In a crisis they will be very hard to enter.
Small local clinics and Veterinary clinics. If its a biological release it will take very few inflicted or radiated patients to shut down even the largest of hospitals. If you want to read a scary bed time story, look up for largest local hospital and find their on file preparedness plan. What you will find if that in the case of Small Pox for example it will only take 3 or 4 to shut the whole operation down. So, you need medical supplies and maybe someone to perform a service to fix that which is broken, these will be the only places operational in the short term. (Dogs leg, you leg really not much of a difference).
Water Pumping Stations: They tend to be in industrial areas with little actual population. They are built to protect the area in case a pipe blows and their power supply is dedicated so it would take a major local disturbance to cut its power. So they are fortified, they will probably have power, they have no one around and now you have water. Hunker down and wait.
Food Pantries-You need food. You need food that will not easily spoil and in a place most people will not think to pillage. It is here. Churches would be the best bet.
Nuclear Power Plants. They are never near populated areas. They have their own armed security force. They have their own water supply to cool the uranium rods. They have limitless independent power. They are fortified-once from attack and once for accidental detonation. They have mandatory food and medical supplies. Some even have air purifiers and bunkers. Problem is getting in and if their staff is first to be affected by whatever has happened, this perfect escape place becomes a secondary detonation.
Lastly Rural College Campuses. They are away from population centers. They tend to be agriculture based so now you have the ability to sustain your food supply. If they are pre-1970 they will have the then mandated bunkers. They will have on site food preparation and supply centers. They have a huge knowledge base. Most have their own armed police force. They have the ability and equipment to sustain complex mechanical and chemical systems. The downside is getting to them due to their location and they are usually unregulated as to entrances and exits. If your running from the biological hazard its going to find its way over to you, eventually.
End of Part One
1 Kings 18:4
While Jezebel was killing off the LORD’s prophets, Obadiah had taken a hundred prophets and hidden them in two caves, fifty in each, and had supplied them with food and water.)