Iíve travelled quite a bit around Europe and there are endless amazing sights to see. As far as a 2 month itinerary, I would recommend Eastern Europe. Granted the travel methods arenít always as convenient as in Western Europe, but thatís what makes the experience all the more interesting! Also Eastern Europe is considerably cheaper than itsí European counterpart and, in my opinion, is less touristy (at least for the time being).
My Eastern Europe top five!!!
1) I really enjoyed Bosnia-Herzegovina; we visited Mostar (and nearby Blagai) and Sarajevo. I found that both cities was a really interesting mixture of European and Middle Eastern styles. Mostar especially is different because it as some beautiful sites, but also many places ridden with bullet holes. Sarajevo has a huge ĎTurkish Bazaarí and many pretty mosques.
2) Croatia has tons of amazing places to visit, but my personal favourite was Dubrovnik!! (Zagreb not so muchÖ)
3) Budapest is a great city; we spent a week there and could have easily spent more time! I didnít visit any other parts of Hungary, so unfortunately I canít offer you any tips for the rest of the country.
4) I visited the Czech Republic over 4 years ago, but I had a great time in Karlovy Vary, which is a tiny town about 2 hours outside of the capital. There were special hot spring fountains around the town and many spas, so it was a rather eclectic place to visit. I didnít really enjoy my lodgings in Prague, but there is definitely lotís of interesting things to see!
5) While Turkey is not always considered as a part of Europe, I would definitely recommend it!! I spent 2 and a half weeks there and I could have easily spent months! I recommend Pamukkale, Goreme and Istanbul!
If you would like more info, I have a travel blog for my backpacking adventure in Eastern Europe.
There are lotís of great things to see in Western Europe too, so here are some of my favourites (and they are likely many other peoples favourites too):
1) Paris: There is so much to do and see in the city, that you can never get bored!
2) Italy: Iíve been to this country so many times, that I am probably biased now, but everytime I return to Italy, I have a better time! There is so much diversity to discover within this tiny boot-shaped country, that if you are travelling to Western Europe, you really must visit it! My favourite cities are Rome (while it is definitely touristy, there are all sorts of unique restaurants that you can find and have your own individual experience), Florence (Or Firenze, thereís just something pretty about this town), San Marino (a quirky little independent country within the confines of Italy), Vatican City (another independent nation, with some amazing architecture and museums), Cinque Terre and Portovenere (if you like hiking, this is a great place to visit!) and there are lotís of other great spots to visit! Half of the fun is having your own vehicle and stopping off in random spots, as it increases your chances of interesting experiences. If youíre on a real historical kick in Italy, itís worth checking out Pompeii and Tarquinia (an old Etruscan city).
3) Amsterdam is a city with a great atmosphere and again there is lotís to see and do. Another great part about Amsterdam is that it is very walking friendly!
4) I havenít visited Spain much, but the one city that I did visit I loved! Granada is a great city both for itsí Islamic heritage (The Alhambra fortress) and itsí free tapas (the only place in Spain for free food with oneís drinks, or at least thatís what Iíve been told). Of course the city has other pluses, but the two above were the key draws for me.
Sorry if I have included waaay too much!! I hope that it is in some way helpful!!