inter rail.
InterRail - travel Europe by train
You buy a train pass for however many countries you want to visit, then just go wherever you want (but you MUST buy it before you leave home!).
The other alternatives are the budget airlines. These are quicker and can even be cheaper than the train. iot you want to spent several days in each place, and the places you want to visit are spread out, air travel; may be better.
try
airberlin.com - Your Airline. Flug online buchen Ryanair.com - Book your cheap flight, hotels, car rental with ryanair.com easyJet.com - book cheap flights, hotels and car hire online Flybe - Cheap flights & budget flights