I agree with most of these posts. I have traveled extensively from the western coast of France all the way to the Slovak/Ukraine border, and lived in France for a year. Western Europe is fun to see and easy to travel in. However you will get a better education in Eastern Europe, although it is a little more difficult because trains and buses aren't as efficient and you will have a harder time finding people who can speak English. If you travel east, try to bring someone in your group who speaks German.
The basic point is that if you want something safe and easy, do the major western cities. If this is the first time to Europe for everyone in your group, that will be enough. If you have some seasoned international travelers with you who understand things like "urban camouflage" and who can quietly slip through a crowd in any country (looking like a flashy American will make you a target for theft) then you should definitely go east. Also if you travel in a group, you may reach a consensus about how and whether you need to always travel in a group, or if you can split and then rendezvous. Chaining everyone together for a month can brew trouble. When you get there, you can easily get pre-paid cell phones to call eachother.
Always watch your wallet in crowded places like subways and train stations. I have seen entire trains cleaned out on overnight routes, even in France. In Czech, I even heard a story of a guy on a train, where a pickpocket used a razor blade to cut through his shirt to access a money belt underneath, and then cut and removed the money belt while he was standing right there. He lost his passport and everything. Consider the "two wallet" system. Be creative. At night in dorm rooms, I had a way to put my wallet inside of my pillow and I slept with it that way. Never, ever, get into a situation where you have to access a hidden wallet in public, thereby giving up its location.
Some of the cities I enjoyed most were: Berlin, Krakow, Prague and Copenhagen. I had my most rewarding (though most difficult) traveling experience in Slovakia. Czech has some awesome smaller towns and cities outside of Prague. Prague is simply awesome, but with all the tourists and being in central Europe, it must be the pick-pocketing capital of the continent. Next time I go back, I want to travel to Hungary and Croatia.