Hey,
I’m full time student in the UK from California and travelling over there is really easy. The UK is well connected by train (i suggest you get a youth rail card for that) and the mega bus (which can be as cheap as 1 pound). Places I’d visit first would be London, then maybe go to the other big cities like Manchester, Liverpool, York, and some scottish cities like Edinburgh and Glasgow. (Don’t forget wales either, Cardiff is really nice)

To visit many cities outside of the UK its really easy and cheap. I wouldn’t suggest Eurostar, but taking RyanAir from London airports is definitely a good way to get around to eastern europe and some western european airports (though the airports tend to be much farther away from the city the further west you go with exception of ireland and the UK)

I strongly suggest eastern europe since its one of the areas in europe that is changing dramatically, and you might want to see it before it all goes. I went to Latvia last summer, and it was awesome. I’m going to visit Croatia (Pula and Zadar) this spring, and Poland (Warsaw and Krakow), Hungary (Budapest), Lithuania (Kaunas and Villnus) and Czech Rep. (Prauge) also seem very promising places to visit.

As for travelling buddies: being friendly, outgoing, and willing to meet people is always a plus! =)
hope this helps

Also, definitely stay in hostels wherever you go… they’re great places to meet young, fellow-travelers.

And, unlike the movies, they aren’t run by psychopaths… just your average friendly, worldly people!