1. Number of homicides per 100,000 people.
2. Number of violent crimes per 100,000 people.
3. Number of people in jail per 100,000 people.
4. Number of police officers per 100,000 people.
5. General availability of small arms.
Using these criteria, these are the top ten least peaceful (or the top ten most violent) states:
9. South Carolina
The thing that I notice first about this list is that most of them are in the South and that most of them are among the poorest states in the country. I'm not sure how Nevada managed to insert itself in the list, but it does have a very high unemployment rate and perhaps suffers from crime related to its gambling industry. But I would definitely surmise that poverty and lack of economic opportunities play a very large role here.
I suspect that the ready availability of guns and the societal worship of the gun also plays a large role. All of these states, I believe, do fit that profile. As if to emphasize the point, here in Houston today a 6-year-old kindergartner took a loaded gun to school with him. The gun fell out of his pocket and discharged, injuring three small children.
This is the kind of society that we live in, where loaded guns are readily available to kindergartners, and they have not been taught by parents to leave guns alone. Indeed, there are actually people in the state of Texas who would seek to have schoolchildren armed. (I don't know if they would extend that to kindergartners, but frankly nothing would surprise me when it comes to guns and Texans.)
At the opposite end of the spectrum, the Institute rated these ten states as the most peaceful:
2. New Hampshire
5. North Dakota
8. Rhode Island
So, if you are looking for a peaceful place, you should head up East. You have several states to choose from there. You had best get as far away from the South and its armed citizenry as you can.