If you're looking for a lot of space, you'll find it in Alaska. You don't need to worry about your neighbors peering in through your windows here; there's barely over one person per square mile in the state on average. The national average is 87 people per square mile. We hope Alaskans don't get lonely!
The flipside of having so much open space is that job opportunities are limited. There's more unemployment here than anywhere else in the country, with 7.2% of the population currently without work.