I've literally spent years travelling in Europe and have no idea of what to suggest to you. That's because you have said nothing about what your interests are. I could tell you where I liked based on my interests but they may be totally different from your interests.
I never understand why people (I frequent travel forums) assume everyone has the same interests and therefore they don't need to mention them when asking a question or when answering one.
There are some general principles that can be shared without knowing your interests. In travel as in many things, less is more. The less you move the more time you actually spend IN places seeing and doing things. That point has been made to you already.
Regarding pre-booking vs winging it, most people are afraid to wing it and find justifications for preferring to pre-book. I prefer to wing it simply because I want the freedom to get up each morning and decide what I am going to do that day. I also find it impossible to know beforehand how much time I will want to spend in any given place. They are after all, places you haven't been to before. I have spent less time than I expected and more time than I expected in places. Who can tell you how long you will want to stay in Paris for? Not me.
It is not (or should not be) a question of quantity. It should be about quality and in that regard, what matters is what you get out of each day you have. People often use the phrase 'I want to see as much as possible' but they confuse the word much with the word many. The way to see as 'much' as possible is to spend your time IN places, not in BETWEEN places. So in theory, the best use of time is to spend it all in one place and not move at all. But most people want to have some kind of balance between what is best use of time and their desire to see more places.
A good rule of thumb for finding a balance is the 'Rule of 3s' which in terms of travel says never spend less than 3 full days/4 nights in a place unless it is just an overnight stop between A and B. It is very difficult to get much more than a very superficial feel for anywhere in less than 3 full days. Some people would argue you need 3 weeks to get any real feel at all.
That rule also helps you understand travel time. Each time you move you more or less lose a day of seeing/doing things. Even if you only move a 2 hour train ride away, you still end up with most of your day lost to the move. So if you count in 3/4 from your total time you quickly see how much you are losing.
For example, if you have 14 days it might look like this. Day 1 fly to A overnight arriving on day 2. Day 2 is in fact pretty much lost due to jetlag. Day 3 is your first actual full day spent doing/seeing things in A. If you then move on day 6 (having had 3 full days/4 nights in A) to B, that means on day 7 you will have your first full day in B and it will be your second night there. Moving again on day 10 to C, another lost day. Day 11 first full day in C and 12, 13 in C with departure from C on day 14 (another lost day.)
So in that scenario, from 14 days you got 3 full days in each of 3 places for a total of 9 out of 14. Five days were lost to travel to/from/between places. That is 36% of your total time lost. Too much for me. Two weeks, two places max is my preference. But it's your time and your dime so my preferences don't matter. I just wanted to point out what it is costing you in time and you are then free to make an informed decision for yourself.
Going back to your interests, you might get some good suggestions if you wrote about what they are. For example, if you love hiking, cities won't cut it no matter how much someone else loved their favourite city. If you like museums on the other hand, what kind of museums?
I once heard 2 guys standing outside the Colosseum in Rome and one saying to the other, 'what's the big deal, it's just a bunch of old stones.' People often go to places because they THINK they should rather than because they actually have spent any time considering what they are hoping to see and do once they get there. Listing cities is typical of this.
On the other hand if you were for example a real automobile nut and maybe a weekend track racer, rather than going to Rome because everyone else does, you might instead prefer to visit Turin and the old Fiat Lingotto factory with the test track on the roof. What's more if you were more interested in how people live life in Italy, it might be easier and probably a bit cheaper to do that in Turin than in Rome.
Visiting the usual, London, Paris, Rome, Athens, etc. list just because others do, may not be best use of your time based on your personal interests.