Let's start with the obvious. If it's a natural disaster like a tsunami or volcano eruption, get out of the way of its path. OK, you already knew that.
Avoid people. In the first day or two as the collapse of society is happening, people still won't be inherently dangerous to you, unless you are fighting with them over resources. But it won't take evil-inclined people too long to start seeing that 1 plus 1 equals 2 and that it is soon going to be every man for himself and the only way to survive will be to steal and kill. People will begin to do this. Increasingly you will need to avoid people. At first, it will be individual thieves. Later, gangs, warlords, and drug cartels will be the ones to watch out for. You will need to avoid other people as much as possible. This means leaving cities, suburbs, towns, even rural areas that can be reached from roads. If you really want to be safe, go to the uninhabited wilderness. That way, you don't have to worry about people breaking into your home. You don't have to worry about people stealing your stuff. You don't have to worry about turning away the starving masses. You don't have to worry about keeping as quiet and keeping such a low profile. It's just less worry. You can focus on providing and surviving.
Avoid nuclear reactors. Nuclear power plants might melt down if they no longer have electricity and people to man them. You will get a Fukushima situation in about 100 different locations all over the US. You don't want to be within 50 miles of them in any direction, 100 miles downwind of them, or using the same body of water as them, so mark those areas off on the map and don't go there.
Avoid large bodies of water and upstream of any large city. When water stops running to people's homes, most people will do the first thing they think of, which is to go to a nearby river or lake they are familiar with. Can you think of the local lake that everybody goes to in the summer? Good. Now don't go there. Are you listening Las Vegas? Don't go to Lake Mead!!
Avoid Mexican border states. Police forces will dissolve. The military and national guard will stick around for a while, but they will dissolve too. All of government will basically dissolve. What are the largest organizations in North America that will be able to maintain some level of continuity? Drug cartels and gangs. They steal and kill to thrive right now. Imagine how strong they will get once they don't have border security and police forces standing in their way? They will be unstoppable. However, they will be hindered by lack of communication just like the rest of us, but believe me, they will thrive in chaos. They will spill over the border and loot the border states. It will be very easy for them. The best thing will be to avoid them for 3-8 years and let their resources run out. Hopefully, they will have infighting and get weak once they can no longer live off of supplies. But I think some of the leaders of drug cartels are smart enough to know that they will need to establish agriculture to continue to survive. Anyways, the point being, avoid them by staying clear of border states if possible.
Avoid downwind of cities. When society collapses, there won't be any firefighters to put out fires. With all the rioting, looting, cooking over open fires, and heating by fires, you can bet that most cities will burn. Skies will turn red and ash will rain down a hundred miles away. It won't be good for crops. I suppose the best thing you could do is cover your crops with plastic sheeting and dust off the sheeting every morning so the sun can get through. Ultimately, it will be best to avoid it as much as possible.
Avoid natural disaster areas. I guess this is almost impossible anywhere in the US. There is some type of natural disaster anywhere, so you can probably ignore this warning, but just keep in mind, you will no longer have tornado warnings or weather men telling you that a hurricane is coming in your direction, etc. Just be prepared.
Now, here's what to look for.
A small water source that is available year round. A private well is best. A small pond or creek is next best.
An area where you can grow food. Take a look at the grow zones (hardiness zones) and give it some thought. Consider if you will need to setup a greenhouse.
An area where you can raise fish. Having a system of aquaponics or aquaculture is one of the best ways to have a renewable food source. Make sure you have the right fish for the temperature of the area. If you need to make the water cooler, put it in the shade. If you need to make the water warmer, put it in the sun, use black lining, or add hot rocks as necessary.
An area where you can raise animals.
An area where you can hunt and trap. Think about what kinds of game live in a given area. Everybody will be thinking deer and wild hog, so don't be afraid to get a little more exotic, like alligator or coyote.
An area where you can fish. If you're not able to fish farm, you can always just fish. Be careful not to kill off the population by over fishing, of course if others are fishing the same body of water, it will be their fault as much as yours, if not more.
An area that doesn't have a lot of pests. Living in our homes, we don't always realize how great a thing it is to not be bothered by bugs all the time. If you bugout and essentially camp out in the wilderness long term, you need to consider this possibility. It sucks being bothered by bugs all day and all night 24/7. However, I guess it's a situation where you have to choose one or the other--the bugs or the cold. Honestly, they both suck.
An area that has good defenses. Think about an area tactically. Does the layout of an area allow you to defend your position well?
Finally, you want to live in an area that is not very visible to the outside, but has great outward visibility. Often, this ideal is hard to find. It is possible though. If you are in a flat visible region, you might consider digging in and lowering your campground. This will keep your whole camp area invisible, but you will still have lookout points at the edges where you can see everything around. Another good location might be to dig in at the top of a hill. It would have great defenses, great outward visibility, but getting water from a position like that would be difficult and might cause you to expose yourself. I can think of a couple of good natural locations that have the best of both worlds when it comes to visibility. One is in Nebraska, and one is in Florida.
The Sand Hills of Nebraska (satellite image above) has thousands of rolling hills. It's a really good place to hide, while at the same time have a good amount of visibility around you. If you were to bugout to this location, you wouldn't want to build your shelter and have your fires on the tops of the hills for everyone to see. You want to be low so you are hidden. But don't situate yourself in a valley/gully. Situate yourself in a solitary pocket like the ones the arrows are pointing to. You'll be able to maintain a low profile, yet have good outward visibility.
In this picture, we're looking at Big Cypress National Preserve in southwest Florida. The land is flat, but we're looking at a system of open grasslands and pockets of trees and bushes. It's not a perfect location, but it's pretty good. What you would want to do in a situation like this is situate yourself in a pocket of trees, so that you are hidden from anyone around, but you will have good visibility looking out at anybody or anything wandering in the area.
When it comes to visibility, if you have to settle for a location, like in the picture of the cabin at the top of this article (low profile, but also low outward visibility) it's important to find a location that is as rural as possible and you will likely be OK.
Good luck hunting for a bug out location!!