If you value your existence and your life, then walk! I am an Air Force brat who did nine years active duty in the Navy. In other words I moved a lot. Eleven states in the first 33 years of my life. I traveled to all fifty states and a few countries. Every one is different, and areas within each are completely different from the part that you live in. Most people that lived in places I have been do not walk any further than a few hundred yards a day. A mile is a "long walk" for most folks. A good portion of the rest walk or run several miles as a work out, but that is with 6 ounce sneakers, shorts and an iPod as their only loadout.
Post SHTF or even during a week without power, you will be subjected to environmental conditions that your body cannot adapt to unless you have experienced it before. The environment that you find yourself in can affect your decision making. Cold, hot, humid or other; these conditions will prevent you from living. You will have to carry a lot of things a long way to make do, even if vehicles are working. You must condition yourself to this level of exertion.
So, go for a walk. Please use common sense and know your limitations. For those with physical limitations, you will have to toughen your mind more than those of us without. The demands on the body are going to be extreme for some even when all parts of it work correctly. I would like to challenge all of you to "honestly" walk 10 miles carrying a light bag. By "honestly" I mean in the clothes that you will be wearing post-SHTF. This will probably be some form of boots, belted pants, long sleeve shirt and jacket. If you can't do this right off, then work up to it but nearly everyone will be able to do it. Ten miles should take 3-5 hours at the most depending your individual condition. Then do this again next month, in a different locale [, over different terrain]. I recommend a 5-7 minute break every 45 minutes as the optimum. [Depending on the weather and personal preference,] breaks of 10 minutes/hour or 5 minutes/30 minutes might work better.
For example, walk 10 miles around your city this month. Next month go to a trail in the woods. Walk. Anyone that has been in the Army or Marines will laugh at this distance. Many people in the Third World walk this far every day just to go to work or school. Then they turn around and walk that far back home. A pace of up to 12 minutes per mile is a good goal if you are in good shape. When backpacking I shoot for 15-20 minutes per mile including time spent for breaks. That works out to a little less than three hours for 10 miles. That is a very comfortable pace I can keep up for days.
The point of this exercise is to learn the techniques that you will need to walk. Everyone can walk, right? Nope, they can't. Most people don't understand about layered multiple pairs of socks, proper lacing of boots, proper waist belt adjustment on a pack and the other items that you only learn by walking (proper is different for each person and can change between the start of the hike to the end of the hike). For the average person with 10 pounds of belly fat, I would start with a 20 pound pack. That is only one gallon of water, a change of clothes, a lunch and a few emergency items plus the weight of the pack itself. You can start lighter or heavier, this is your challenge. Bring extra socks, moleskin, an ace ankle wrap and Band-Aids the first few times [or whenever you switch to a new set of footwear]. You might need them before you make it back.
Please only walk one day a week, to begin your training regimen. You will get serious blisters if you are not used to it and try to walk 3 or 4 days in a row. Just in that first walk you will learn what you like and don't like about your shoes. For instance, you may find that you need to wear different underwear, an undershirt, and perhaps a different hat. You will realize that it isn't that hard and it will encourage you to go further. Once you build up calluses [, stamina] and find your individual pace, then you can go all day. Now you can get through the long walks that are inevitable when SHTF and your body will remember. This conditioning will free up your brain to focus on decision making-- unimpared decision making. Weather extremes can still get you but you have a baseline experience level. I recommend that you walk year round to learn how the weather affects you (But I realize this is unlikely, especially in extreme cold and heat for many people.)
General guidance for a maximum backpack weight is 1/3 of your body weight for medium distance hikes. 1/4 of your weight (1/4 of 200 pounds is 50 pounds, in my case) is far more comfortable. This may seem like a lot but with the right boots/socks and pack it actually is easy. And since you are already walking 10 miles straight now, you will quickly find out what qualities to look for in your gear. Some things can be fixed for free. For example, I don't lace the top holes in my boots. This lets my feet breathe a bit more. I have learned how to load"my pack for maximum comfort.
Okay, now for the good news. Once you can do this for a few days straight with about 20-30 pounds on your back, you don't have to do it all the time to maintain the conditioning. I find that a 5-6 mile walk once every week or two with a 15 pound pack and "first line gear" maintains my long distance conditioning for months.
Long distance walking does not replace aerobic conditioning, it simply allow yours feet to get used to the abuse. You still need to aerobically condition your body for maximum cardiovascular health. In parting, I was amazed at the amount of heat produced by my feet the first time I walked ten miles on a hot day in boots.