I would suggest you to rent a car and go on a road trip. There is no borders between the European countries and will have the best and unique and authentic experience of your life. You need to apply for international driving licence and then you are good to go. I went to Europe last December. We rented a car in Poland and went on a road trip to Amsterdam through Germany. Simply amazing. Now that you have a car, you can book rooms outside of the city and it will be super cheap compared to living in the main areas.
1. Try and keep a mix of countries with different terrains Mountains (Swiss/French/Austrian Alps)+Beach (Italy/Greece/Croatia/French Beaches) +Historical cities (Rome/Paris/London) and keep 2 days per city. 2. Pick a region between eastern/central and western region.3. Take the euro pass for euro rail for luxury long distance travel and Bus travel (Flipbus) for shorter distances.4. Book Flights and Hotels near the city centre and keep open itineraries and cover things at your own pace. But do keep a list of interesting places you want to go and experiences to give your tour some structure.Hope this helps.