Most countries are very particular about non-national people who want to work in their region and do not allow others to just show up and start job hunting. In certain parts of the world, it is next to impossible for many of the nurses who are already citizens to find jobs. Many parts of Europe are over-supplied at the moment.
You would also have to prove language proficiency, among other things. AND most of the countries that would even consider taking a US-educated nurse would want a minimum of one year on he job and probably more. And that's if you are a BSN and if your curriculum covered everything the other country's licensing and regulation people required.
No place I know of wants to train a new nurse just out of school. That's a hugely expensive commitment, and not one they are likely to even consider if they know the person is likely to return to the States after a short time.
I don't mean to rain on your parade, but, with so many hoops to jump through and the experience requirement, this just doesn't sound like a practical idea.
Perhaps, in the future, when you have the first few years of nursing out of the way and you are comfortable with your knowledge and skills, you could volunteer with a group like Doctors Without Borders or something similar and donate a few weeks of your time to gather some first-hand knowledge of what it's like to work in an area that you are completely unfamiliar with. You will be able to assess whether this is something you can do for a longer term, and you will probably make some wonderful friends and memories.
I'm sorry that what you have planned will probably not work out. Don't give up your dreams, though. Who knows where they will someday lead you.