3 weeks in Italy

Next September/October I will be spending 3 weeks in Italy and obviously would like to visit Rome, Florence, Venice, Amalfi Coast and the Cinque Terre. Does anyone have any itinerary suggestions and how long to stay in each place. I will have about 19 days in Italy before heading to France.

where to begin?! Well Venice for a start, partly as its the easiest to reach by most cheap flights and its the most expensive so get it over and out of the way first.
you can spend a day walking the canals and seeing the sights of Piazza San marco and the Rialto. give yourself another day to do the museums and the islands of murano and burano, you could also add a third day and do a day trip to Verona which is well worth seeing.
Reccommended is to take the train. its easily the most convenient and cheapest way point to point, plus the locals are great to talk to on the way, very friendly and chatty.
Florence will need at least 3 days but don't leave out the smaller towns outside.2-3 more days to see Lucca, Siena, and other tiny tuscan towns like san gimignano and Montepulciano and well worth the time out of the big cities. you could add another half day and see pisa, you really only need a few hours as once you've seen the tower thats it.
rome needs at least 5 days to get round everything comfortably without rushing, it can be done in 2 but if you have the time why not enjoy it.
head south to the Amalfi Coast for 2-3 days, it will still be warm and sunny down this way so get out and explore Sorrento, Positano and maybe some of the coastal islands (capri), preferably on a scooter. you'll be in the shadow of Mt Vesuvius so don't miss the opportunity to visit pompeii and/or herculaneum, the excavated roman cities. these need a half day to get round each. Naples gets a bad rap but if you go there with your wits about you (and outside peak tourist time as you are) you shouldnt have too bad an experience. its no huge loss if you miss it though.
heading back north towards Cinque Terre you can spend 5 days there discovering the 5 villages and the walks between, it will be hard to leave actually, a totally different pace of life. no rush to do anything.
which leaves you in perfect position to carry on northwards to france. the western coastline scenery of italy is awesome all the way up to france.
buon viaggio!