Are certain areas of the world, specifically within the United States, more or less rational than others? If so, which ones and why? I am trying to determine what parts of the country would be ideal for me to live in the future and any help would be greatly appreciated.
Whether people are more rational is not necessarily a good reason to live somewhere. That said, here's some data that might help:
If you think that religion is strongly correlated with a lack of rationality then looking at how religious the population is might help: here gives the fraction of the US by area which identifies as "no religion." But note that "no religion" is potentially very different from atheists. When you give people the options of "no religion" "atheism" and "agnosticism" the "no religion" looks demographically quite different. For example, see this recent Pew study which shows that atheists/agnostics know a lot more about religion than people who identify as "no religion." This is likely due in part to the fact that "no religion" includes people who a) have not thought about the issues much b) don't know what the word "atheism" means or c) identify as "not religious but spiritual" or something like that. That last should also include Protestants who claim to not have a religion but have a personal relationship with Jesus (the GSS data suggests that in some areas especially the South this isn't that uncommon). Note also that there are other complications, such as many Jewish atheists who would if put down religion would say "Jewish" but have an allegiance that is more cultural than religious.
There's unfortunately very little data about whether atheists are more likely to be rational about other issues. Although note that some of the GSS data suggests that agnostics are less likely to believe in astrology and a handful of other pseudoscientific ideas than atheists. See this post.
Another possible weak proxy might be fraction of the population with a college education. According to the US Census data, (which I can't track down at the moment) the educational attainment percentage tracks pretty closely to the "no religion" graph linked to earlier. Note that the GSS data confirms this also.
So both proxies give somewhat similar estimates. I don't think either of these are terribly great proxies though.
I suspect "atheists", "agnostics" and "non-religious people" describe people that have roughly the same beliefs about the world (in terms of expectations as to what physical things will happen), but have different signalling; atheist signalling that they are affiliated to scientists and hostile to religion; agnostics signalling that they are wise and cautious and not hostile to anybody, "non-religious" just not signalling affiliation to any group based on religious opinion.
Arguably, the same could be said of many moderate and educated religious people: they have the same actual expectations about the world, but choose to affiliate with a religious group for mostly social reasons.