The problem being that you're American (used to high salaries) - this greatly limits where you would be happy. I was in the Republic of Georgia recently, and fell in love with that culture. I could easily move there and not really worry about their low wages (or their proximity to mother russia)!
It's an even smaller world when you're American (WE'RE ALL SUCH SPOILED LITTLE BRATS).
I'm American born too, and just as spoiled as the next one!
Stay in the usa, please please, stay in the usa
You do need to consider if a country will allow you to work/live there for years. NZ might be perfect, but it can be difficult to get a visa to work/live there. Check.
I have to agree with Santa Fe NM. Great year round climate, beautiful city, very few of the problems many large US cities have. Give it a look before heading off around the globe. My 2 cents.
Looking at the criteria that you have I would say Australia is one place which you could go! I'm not entirely sure about the visa application process, however I'm sure it would be fairly similar to that of NZ. Australia is a mainly christian country, while also having large multi-cultural aspects to it (Melbourne especially, and it was voted #1 most liveable city in the world a number of times). Australia really is a great place to live, any of the cities are beautiful, and they are all close to mountainous regions that you listed in your criteria. I really would consider this as an option.
Best of luck with everything!!
I recommend Adelaide in Australia because it is known for its greenery, cleanliness and in a recent survey adelaide is choose to be the most crime free city in the world.