Western Europe several months, multiple countries - Group Travel

Hello, My name is Mariam. I am 22 years old. I was planning to study abroad at an American University in Rome for my last semester of college, from January 2013 to May 2013. Then I realized I can take the last two classes I need to graduate online therefore do not have to be attached to one location in Europe. I cannot choose just one city to visit so I’d rather just backpack my way through!! I want to see all that I possibly can in the months from January until May before I have to begin physician assistant school.
I included a list of some of my dream destinations in Europe under the highlights section I would like to hit up as many of these as possible and am extremely open to suggestions!!
I would like to travel on a budget, staying in inexpensive hostels and such. We could take trains to wherever our heart desires!
I am very open to new experiences and would love to have someone to travel with. I am easy to get along with, caring, and looking to explore the culture, history, and beauty of Europe. Please let me know if you are looking for a similar plan and we can plan together!

Western Europe several months, multiple countries