Suggestion, with "a week or so" of travel time consider the value of seeing less of Europe and more of a destination.
So many people try to do, like, 10 countries in 10 days and what they get to see is a lot of airports, train stations, bus terminals, and tourist sites which you can easily see via pictures on the internet. Can you imagine trying to see the United States in 10 days? Even in Europe trying to see a whole country in 10 days is probably trying to do too much.
Consider going to one place, one city, and instead of being a "tourist", be an "explorer". "A week or so" is still not enough time to really immerse yourself in a place and get to know the place more like a local, but at least you have the opportunity to enjoy more authentic experiences. You may even make some friends.
Also, if you've already got friends in a desired destination, go to that place. They already know the place and you have a better chance of getting to see the city and surrounding region more like a local.
Yes, use the "Hop On, Hop Off" bus for your first day to get an overview of the city. After that, use public transit (in those cities where there is good public transit). Be with the people. Don't be afraid to talk to people and get to know people. You just might find yourself invited to a group dinner at a home and all of a sudden you've got a new group of friends.
Enjoy your trip whatever you do and wherever you choose to go.