When I was running my roots travel business, I took a survey at the California Family History Expo. The survey was an unscientific sampling of those who stopped by my booth, but one thing was certain. For international roots travel, the countries most people were interested in traveling to were Ireland, Scotland and England.
The reason is clear. These countries provide an excellent place to start visiting your family's past. They are foreign, but not too foreign. English is spoken, making it easy to communicate. It is fairly easy to get around by train or by car. Plus, each place has a robust system of bed and breakfasts to put the roots traveler close to those small villages from which ancestors always seem to come.
Not only that, but for those wishing to put their family's roots in place in history, each of these countries offers centuries of history one can see and explore, making the roots travel experience that much deeper. There are enough museums, houses, and historical buildings to develop a well-rounded vacation including roots travel and general historical travel.
So if you have English, Irish, or Scottish ancestry, consider a trip to one of those countries as your first foray into international roots travel. You won't regret it.