With two months, you can cover the entire region, but it will still be a bit of a 'Best of' trip. Skyscraper-filled Frankfurt-am-Main, Germany, is most useful as an air hub, but you may want to spend a night. From there, shake off jet lag at the chi-chi spa centre Baden-Baden before exploring the bucolic towns of the Black Forest. Just across the Swiss border, the cobblestone streets and cafes of Basel await. Move on to the modern art and ancient architecture of the capital, Bern.
Soon the Alps beckon: Interlaken and the Jungfrau region have some of the most extreme mountain scenery around. Check out the cafe scene of Zürich before crossing the spine of the Alps and getting ready to imbibe in the beer halls of Munich. Spend a few days, so you can bus it along the Romantic Road and see the fantasyland-like Schloss Neuschwanstein in Füssen. Next stop is the baroque, music-filled city of Salzburg. Then it's south into the Julian Alps and picture-postcard, lakeside Bled, Slovenia.
The lovely little capital of Ljubljana is also worth a stop before you ride the rails on to impressively imperial Vienna, Austria, for a couple of nights. A riverboat ride along the vineyard-laden Danube Valley is a worthy detour before travelling downstream to the bathhouses and bars of Budapest, Hungary. To the south, the architecture in Pécs retains some remarkable Turkish relics.
Heading north again, myriad Old Town cafes in Bratislava, Slovakia, make a good pit stop en route to the Tatra Mountains. On the Slovak side, the most atmospheric midmountain village is Ždiar, in Poland, it's Zakopane. Hike rugged area trails before you continue to Kraków, one of Europe's prettiest Old Towns, near the notorious Auschwitz concentration camp. A local favourite and another lively Old Town, Wrocław is next, then Dresden, Germany, a restored city that exhibits some impressive art.
The whole of Czech captial Prague is like a museum, so you'll want to take several days wandering its neighbourhoods, or side trip to spend a night in even more medieval Český Krumlov. From Prague, you can return to catch a flight in Frankfurt-am-Main (7½ hours by train), or exciting and edgy Berlin is only three hours north by fast train.