Bernd seems to be the only one thus far who understands where Eastern Europe is. Paris, Rome, London, Venice, Santorini, Florence... none of those are in Eastern Europe. While technically Greece is located east of mainland Europe, culturally it is not "Eastern". Greece is one of the original 15 member nations of the EU and is culturally unrelated to the Slavs, Dacians, Magyars, and other groups that are typically associated with cultural and linguistic Eastern Europe, and is usually not included as an Eastern European country (any more than Turkey is).
Of the countries that most people would consider to be "Eastern Europe", I've been to Poland, the Czech Republic, Slovakia, Hungary, and Slovenia. I would love nothing more than to get to see other countries in Eastern Europe, though; two on the top of my list are Romania and Bulgaria... but I wouldn't mind getting to also see Croatia, Ukraine, and the Baltic states too.
From personal experience, I can recommend Prague, without a doubt. Bratislava is another favorite. Budapest--no contest, another must see. Ljubljana (Slovenia)... it's smaller and quieter but I was very fond of it, and it was a pleasant surprise--and is less busy and less expensive than just about any modernized Eastern European capital you can name. In Slovakia (other than Bratislava, of course), I visited Devin, Trencin, Cicmany, and Bojnice--and I would recommend all of them.
There are many places in Eastern Europe I haven't seen but would potentially recommend simply because I'm interested in seeing them, too. The best thing I can recommend is to read about each country, and if possible, each city you're thinking of in those countries, to see what interests you.
Lived in Europe for over three years, did a heck of a lot of traveling during that time.