Venice, Florence, Positano ?

Where are you flying out of when you return to the states? Rome, Florence, Naples?

You can always go to Florence first then down to Positano. Or you can consider the night train from Venice to Rome and early train to Positano and do Florence last if you are flying out of there.

You can fly into Venice and out of Naples (you will fly into another European city, possibly Rome, to connect with an international flight) or fly into Venice, take the 2+ hour train ride to Florence, then go to Positano and take a flight out of Rome (use ferry/train or bus/train combos to get from Positano to Rome).

A freccia train from Venice to Rome is four hours, I wouldn't want to stretch that into an overnight train trip.

Any hotel recommendations for Positano? Is it worth driving down to Positano?

If you want to spend time on the Amalfi Coast ("AC"), Sorrento is the best base. Having a car there is more of a disadvantage and Sorrento is the best-connected town to see the rest. Take a high-speed train to Naples, then the local Circumvesuviana to the end of the line, Sorrento. You can take the train to visit Pompeii, Herculaneum, even Naples. There are bus and/or ferry connections to Positano, Ravello, Amalfi, Capri.

Florence is on the way from Venice to the AC, so it makes sense to stop there in the middle, especially if your return flight is from Naples - or even Rome. It's just a couple of hours by train from Venice to Florence, but it will take a 1/2 day to get from Florence to the AC.

How much time you spend in each place depends on your interests. I'd say 3 full days in Venice to start. Considering jetlag and lack of sleep, maybe one or two more. Florence is all about Renaissance art and architecture. If that turns you on, 3 full days won't be nearly enough. If it's not your cup of tea, then 1 full day to see the highlights. If you want to explore Tuscany without the "arty stuff" consider staying in Siena for 3-4 nights, visit San Gimignano and Florence as day trips, take a wine tour, or rent a car and stay in an agriturismo for 3-4 nights or more.

I could spend a week or more just on the AC, with day trips to all the places (and others) I mentioned at the beginning.

So many wonderful choices, so little time! Whatever you decide, it will be a great trip.

Sorrento is convenient, but it's not on the Amalfi Coast. Just depends on whether you want to stay on the AC or daytrip in.

There is a very good connection by train between Venice and Florence. From Florence by train to Naples probably with change in Rome. For schedule you can check Deutschebahn website or Trenitalia. From Naples by train Circumvesuviana to Sorrento. I agree with Chani that Sorrento would be better base than Positano. We took boat from Naples to Sorrento. Much better choice than hot train without AC. It was beginning of October. From Sorrento you can get to Positano by bus. Very stunning and scenic ride. Be on the right hand side of the bus. Or you can go by boat. If you decide for Sorrento as your base you can do day trip to Amalfi by bus, back by boat and stop for several hours in Positano. Some other day you can go by boat to Capri. If you have still more days you can get to Pompei by train. Very good source of information is Rick Steves book: Italy. We got also out of touristy area looking for my spouse ancestors and for information on travel and accommodation I used google.