I'm just going to put it out there that Europe is my favourite place to travel.
Maybe I'm just a romantic but you really can't beat how much history, diversity & cultural variation Europe has on only 2% of the earth's surface.
It was the first place I explored and it did not disappoint. Public transport is super easy and surprisingly cheap considering Europe isn't really a backpacker destination.
The greatest thing about Europe (UK excluded) is that thanks to the Schengen Visa Agreement which comprises 26 mostly-Western European countries, once you have a visa you can freely cross from one country to the other without any hassles. This includes student and tourist visas.
When I au paired in the South of France for 6 months while studying French, I had a student visa and managed to easily travel the length of Italy, most of France, Greece and Holland all in that time.