Not counting travel 45 – 60€/day. Add your travel on top of that (averaged in) and you’ll probably end up spending a total of 80€/day, multiplied by 22 days is 1760€ total. Here’s how I got that number

Hostels cost anywhere from 15 – 20€/day
Food will cost you anywhere from 10 – 20€/day
Your mode of transportation will be the biggest factor determining your budget. Some places you visit, you will be able to walk everywhere, others you will have to take a bus (about 3€ round trip depending on the the place you’re visiting. Traveling from country to country depends on whether or not you fly or take the Eurail, as the prices will differ greatly depending on how many countries you plan to visit. I would suggest looking at my blog post about the Eurail at http://europeforstudents.blogspot.com/2011/06/all-about-eurail.html. You may actually find it’s cheaper to fly with a company like RyanAir (http://europeforstudents.blogspot.com/2011/07/fly-away-plane-travel-in-europe.html).
Lastly, you have to take into account that it will cost money to do some things, like a bike tour in Amsterdam is 20€.

For more about how much money it costs to travel abroad, check out my blog post http://europeforstudents.blogspot.com/2011/11/frequently-asked-question-how-much.html It’ll go much more in depth than I can here and it’s all from personal experience. It’ll also give you inside into what method of travel you want to use, how not to get pick-pocketed, and other ins and outs you’ll need to know to make your Europe travel more enjoyable.