When it comes to the actual travel side of things, I would say go for interrailing or coaches. Both of these are far cheaper then planes and is a much more sociable way to travel and meet new people. You can find some really good deals online if you look around, especially for Europe, http://www.interrail.eu/ s a fantastic sight where you pay for one ticket, and you can get three days of travel to wherever in a month, or whatever you choose. It’s a great way to travel, and make stop points if you want to see more then one city in a country.
This is a super obvious one, don’t pay for hotels. They may look more luxurious, but if you are travelling and sightseeing, chances are you won’t be spending too much time in your room. Try hostelworld for good recommendations, find one’s that are reasonable cheap, near where you want to be with basic facilities, wifi, showers, kitchen, air con (if you’re going somewhere hot). Not only are hostels a lot cheaper, but the majority have a much more sociable vibe then hotels, and again with coach or train travel, you’ll meet other people travelling.
Hostelworld also offers a free city guide, if you book with them, making your travels a little more easy going.
Have a look online for a few ideas of what you want to do there, a lot of interesting stuff is totally free, and if you pick the right day (usually Sunday or Monday in Europe) entrance to museums are free.