Are you saying you've been to all of these places before except the Cinque Terre?

Most of your questions have been asked and answered here many times. How to reach Positano, how to travel Positano-Rome, where to pick up a car for Tuscany, whether to keep the car while in CT, etc., etc. Some answers depend on your budget and personal preferences. Maybe someone will take the time to list the options for you, or you could do some searches. (See "Search the Forums" at the top of the screen.)

I will comment that driving from the Cinque Terre to a lake and then to Venice would be easier than taking trains, but you won't be able to see much of any lake in only one full day. You'll spend at least a 1/2 day driving to either Como or Maggiore (on 9/23) and then at least another 1/2 day driving to Venice (on 9/25).

Sept. 8 arrive at Naples airport 10 a.m.( travel to Positano HOW?)

Hire a private car to take you. At that time of year, jet lagged, negotiating the pubic transportation options with luggage is daunting.

Sept. 8-13 Positano La Fenice (Day trips up to you, but Pompei is too far. If you want to see it, see en route to Rome. You can park your luggage at the entrance to Pompei. Get a driver to take you to Pompei.)

Sept. 13-17 Rome Apartment near Piazza Fiori (How to get there from Positano?) - It is Campo de'Fiori, and you should have a driver take you the Naples train station (or Pompei if you want to see it).

Sept. 17-21 Rental near Siena (Pick up rental car -where in Rome?Drive from Rome.) Better to take a train out of town and pick up your car nearer to Siena. Orvieto or Chiusi are both convenient for a scenic drive on the way to Siena.

Sept. 21-23 Cinque Terre (Town? Hotel??)Should we drop off rental car and take trains to CT and then to Venice or drive across and stop at one of the lakes? -- Since you are going to the Amalfi, you might consider going to Lago di Como for a different kind of stunning beauty. If you insist on le Cinque Terre, consider staying in Lerici with the car, and visiting le Cinque Terre by boat if the weather is nice. If it is not nice, day trip with your car someplace else.

It is a long boring drive from the Mediterranean to Venice if you wish to go to le Cinque Terre. Rather than try to squeeze in one of the lakes, pick a pleasant petite city with great food and things to see in between the Med and the Adriatic to spend a night. The choices are endless, but Parma, Modena and Ferrara are all good candidates.

Thank you for your thoughtful replies. Any more suggestions? Can anyone recommend a driver to use from Naplesto Positano?

>>>Sept. 8 arrive at Naples airport 10 a.m.( travel to Positano HOW?)<<<

You can take the Curreri bus (10€)from the airport to Sorrento and change to the Sita bus (about 4€) to Positano.

http://www.curreriviaggi.it/inglese/E_index.html

This is the driver we used and would recommend him http://www.cuomonet.it/

I agree with most of what pizzo said.
I highly recommend the company we used to go from Naples to Positano -- Eurolimo. Prompt, courteous, fair price. You can take the bus, but I'll leave it to you as to whether that's the sort of thing you want to do after a long plane ride.

Getting to Rome: Depends on how much you want to spend, and your tolerance for public transportation. You could take a bus or hire a driver to take you to the Sorrento train station. From there, train to Naples, then change to train to Rome. Then a taxi to your apt. It's not bad. If you want more convenience at a higher price, follow pizzo's rec to use a driver to take you to the Naples station.

I think you could do Pompeii as a day trip from Positano. You could hire a driver or take public transportation. Again, depends on your budget. Some people spend all day at Pompeii; others are satisfied after 2-3 hours.

The Lakes would be nice, but I agree that trip might be a bit much, and you could spend the time at some other picturesque place that's not so out of the way.