Well..it depends on the time your gonna spend travelling around...
For a 15 day trip or more I would recommend: Central Europe or the Mediterranean Sea.
Central Europe:
Paris-Brussels-Brujas-Ammsterdam-Hamburg-Berlin-Prague-Munchen-Vienna-Salzburg-Zurich
Mediterranean (Great in the summer):
Barcelona-Nice-Marseille-Monaco-Venice-Firenze-Rome-Napoli..if you have enough budget...take a flight to Dubrovnik (Croatia)-Athens-Santorini-Mykonos-Istambul (Turkey)-Mersin (Turkey).
Must see places??!!!!...EVERY CORNER has something interesting to do.....just ask for a tourist map of teh city at the Airport or Metro Station and do your itinerary....please: DO NOT LIMIT TO SEE those touristic spots at the map...walk through the city and see everything......
At the hostels you may find a lot of backpackers that always have some experiencies of the places recently visited and they will gave you tons of information: Wheres the cheapest place to eat, the best party, the best cafe, free internet, etc etc....
Visit the page hostel.com.....and make your room reservation in advance, you may find better prices......For Cheap Meals, try to find the supermarket next to your hostel and try to eat at the hostel....Travelling by bus in Europe may be cheaper but I prefer to do it by train (visit the eurail page and see the packages).....another way to travel in europe is by plane (faster and sometimes cheaper but you can not see the beutiful landscapes indeed)...check it out the webpages of easyjet, ryanair, or airberlin.
Get some Euros in cash before you leave your country,,,you may find better exchange rates....and its cheaper if you make a few cash withdrawals of big amounts...than if you are making small withdrawals everyday at the ATM's.....If you have a credit card,,,its a good option...
Scandinavia is beautifull but its extremely expensive....as well as London......not for budget travellers....
Prague its very cheap and you may find rooms/beds from US$10 a night..and the city is great!!..
Hope ot helps...and enjoy your trip
