Rome - Incredibly well preserved history and sight from Ancient times all the way to modern. So much of Europes history can be found in Rome as the capital of a vast Empire anciently and the spiritual capital of Europe through the Middle Ages. Plus it has a great energy and food.
Prague - Absolutely stunning city. It's just a blast to visit. Has preserved it's Medieval and Baroque importance very well. Not only to you get a taste of Eastern Europe as it is a Czech city. But you also get a feel of Western Europe as it was a city dominated by Germans from the 14th - 19th centuries.