Whether staying in the US, or traveling overseas, don't forget about the train. Within the states, you can take Amtrak to most major US cities. If you plan to visit multiple cities within Europe, a Eurorail pass is your best bet for economic transportation. They can be bought through either of the following sites. After you book the ticket, you are going to need some place to sleep.
Hostels are like dorm style hotels.
Accommodations are usually simple, but you can't beat the price. Their site also has a good explanation on hostelling, how to travel safely, and how to plan for your trip. You can visit the OIE's Study Abroad web page for additional links. You can also apply for an International Student Identity Card which offers basic travel insurance, as well as student travel discounts. Stop by the office, or visit Council Travel for more information.