This is a common question for most people. You are walking around and all you are finding are Pidgeys and Weedles. This seems to be the case for everyone across the world. The developer of the game has stated that they intend on making the locations of some Pokemon specific to certain locations of the world. So far this functionality has not been confirmed by anyone. Most people have been able to catch a whole array of different Pokemon across the world and the region does not seem to affect the Pokemon that you find.
What does happen in terms of location is the base element type of the Pokemon that spawn. For example, you are most likely to find water type Pokemon when you are near the water. Rock Pokemon are more common in rocky areas etc. This is not highly accurate as there have been cases of water Pokemon showing up in locations that have no water, but in general the location affects the type.
So in short, at the moment, you do not appear to have to fly to other countries to get all Pokemon. It is meant to be implemented eventually, but right not it does not count. As long as you level up, you should eventually start coming across the more rare Pokemon in the game.