I use Kayak all the time. It will show you a lot of options and then you book through the airline itself or whichever site has the best price. You don't book anything through Kayak.

If you are worried that you won't get the best rate through booking.com you can spend an extra few minutes and check the rate through the hotel's own website, then pick the better rate.

A flight into one city and out of another is called an open jaw flight and is much more efficient than working your way back to the first city at the end of your trip. Doesn't usually cost more than a round trip in and out of one city. On Kayak you can find these itineraries and fares by checking multi-city, as Isabel suggested.

I usually prefer to book directly with the hotel (altho I have never had a bad experience using a booking site). I usually do my research using Tripadvisor, then contact the hotel directly.

Has anyone mentioned an overnight train trip as a possibility? Some people like that option for going city to city, others hate it, but I'm a fan. It is a pretty unique European experience.

Me, I'd choose Paris, Venice and Rome unless your guys? are big art fans. Venice is so amazing - Florence is IMO a bit of a ho-hum Italian city, again, unless you want alot of museum time. I would not try to cram in Barcelona, much as I do love that city. I don't think any of the cities mentioned deserve only 2 nights!

I used booking.com recently and got the best rates I found anywhere and it is a user friendly website, but first things first.
Go step by step and this won't seem so hard?
1. Pick two most important cities - bookends of your trip. (Paris and Rome?)
2. Book airfare into one and out of the other.
Good, done with that.

3. Decide which interim city and how to get there. Book a flight if necessary from Paris to there.
4. Book hotels.
5. Relax and enjoy planning your sightseeing. Assign some of this to your sons.
6. Book any local tours you want and order tickets to museums you are absolutely certain you want.

A tour group will NOT please your sons!!
As someone else intimated, 4 adults can certainly plan a very memorable and worthwhile trip.

And as a point taken that all opinions are personal, I prefer Florence over Venice, although visiting the latter would certainly be fun and interesting. Just not for days and days.

You will get all sorts of advice on where to go. I don't think Florence is ho-hum at all. I would choose Paris, Florence and Rome but it is not my trip just as it is not the trip of any of us providing advice. Do lots of research - it is part of the fun and makes your trip so much more rewarding. Then pick your cities and do, as recommended, fly open jaw.

Sassafrass provides very good advice. Once you have the outline planned, you can focus on the details.