I have traveled to all 44 of the countries in Western Europe. The diversity of cultures is extraordinary, and the remarkable history of the region is so inspiring. I can't say that any one country stands out above any other. They are all so unique and different from one another. Americans who are considering international travel will find that Western Europe is a great first step. It is very westernized while still quite different than the United States, and definitely a "must see."
The many countries comprising Eastern Europe and Eurasia were very repressed before the fall of the Soviet Union. Since then, they have become popular places to visit. From Belarus to the north, all the way to Macedonia, Albania and Bulgaria in the south, the now-independent countries have been undergoing revitalization. The area has some of the most interesting architecture in all of Europe and has been successfully promoting tourism. The cost is still less than traveling in Western Europe, and I encourage people to go there soon, before the cost inevitably rises.