ellie_pol, am thinking the answer to your questions really depends on how much you want to see in each city visited. My preference is to do some research and narrow down what I want to experience in each city first, then set up an efficient itinerary that includes everything, or at least as much as possible. From there, I determine how long I want to spend in each city.

I'm guessing the concern folks like janisj and jamikins have here is that cities like London and Paris have easily a week's worth or more of great attractions, depending on one's interest. Given what I want out of traveling, that's a concern to me as well. However, if you only want to get a taste and hit a few highlights (especially with an eye towards going back again another time to explore further), a speed itinerary similar to what Palenque suggests could also work.

Will also second the idea of taking overnight trains between in-Europe destinations to maximize your actual sightseeing time.

To me Europe is much more than the mega-tourist cities, where yes you can spend weeks and never see everything of interest - but if you only dwell on a few mega-tourist cities then IMO you miss the essence of a European trip - for first-timers i do think 3 days - 3 full days is enough for any city and spend some time yes taking trains and seeing the lay of the land as well. Or else you see Paris and London perhaps and only airports.

paragash - the overnight trains between Geneva and Venice have been abolished - but you are right that there are literally hundreds that do run - save a night's hotel cost and arrive bright and early - can literally cross Europe at night.