I'll add my voice to the pick one country suggestion. 2-3 weeks is not enough time to really see all the countries that you are listing. I spent 3 weeks in Italy last fall (Sept-Oct) and it was still tight to see the things we wanted. I highly recommend doing most of the travel by rail though a car for a couple of days can make some more rural locations more easily accessible particularly since you are on a tight travel schedule. I rented a car for 3 days out of Florence (got a Smart for Four) with a return in Siena. This allowed us to hit the small Tuscan hill towns. If I was retired and travelling then I wouldn't have bothered with the car but would have taken the train/bus to the towns.
You can also plan when you travel between towns to maximize your time. For Italy we would travel early in the morning often catching one of the very first trains. That way we would arrive no later than mid-morning which would give us plenty of time to find a hotel, freshen up and drop the bags and then grab lunch before having an afternoon in the new city. For longer trips (some we did in China for example) we would take the night train and sleep our way between cities.
Travel light. Let me say it again travel light. It's so much easier to get around if you aren't humping along a couple of giant suitcases each (though I saw some poor schlubs trying). A backpack makes an excellent choice - if you want get one of the ones that converts into a suitcase. This makes riding the busses, getting to the train, getting around the station, getting up the stairs, etc. all much easier. It also makes it easy to leave your one bag at the baggage check at the train station if you want to just look around the city for a couple of hours (we left the bags at the station in Pisa and just spent 2-3 hours in the city before going back to the station, getting the bags, and moving on). I have a couple of good links on this but they are at home - if I remember I'll post them later.
Another thing to consider is your flights. The way most people plan they fly into and out of the same city. This often leads to wasted time travelling back to the arrival city. I've made good use of what are called "open jaws" tickets - fly into one city and out of another. On my Italy trip that was into Napoli (Naples) and out of Venezia (Venice). On a previous China trip we went into Hong Kong and flew out of Beijing.
An interesting option posted a while back by ESRBob is to take a canal boat vacation. You rent the boat and cruise the canals of a particular region (Britain, Benelux, France, etc.). Here's some discussion of that -
http://early-retirement.org/cgi-bin/yabb/YaBB.pl?board=misc;action=display;num=1095867219;start=1
Finally, take some time to learn the basics of the language before you go. It will make the trip a much more pleasurable experience. Your local adult ed French or Italian or German or whatever class is cheap and will help.
P.S. If you do go to Italy then I agree with Flowgirl about Cinque Terre. Don't book a hotel there but arrive early enough in the day (better still not on a Friday or Saturday) and you will be able to find a room in somebody's house. We stayed in a home with an sea view belonging to a charming old widow who gave us the lowdown on which restaurants to eat at (and avoid) plus she shared some delicious home-made limoncino!
