10 nights in Italy

Add one night to Venice. Borrow it from Rome.
VENICE: 3 nights
FLORENCE: 3 nights
ROME: 4 nights

You should seek an open jaw multi city flight
going: PARIS - VENICE
returning ROME - USA
It is best to fly out of Rome than Venice. Venice airport is difficult to reach from the city center (which is in the middle of the water) and flights to the US (always departing in the morning) would likely require a connection in a European hub, hence you would need to get up at around 3am to make a flight out of Venice at 6:30-7am. Rome airport is much closer to the city (30 min by taxi or train).

Venice to Florence: 2h by train
Florence to Rome: 1.5h by train

Two train companies to choose from:
www.trenitalia.com
www.italotreno.it

If you have never been to Italy before, I wouldn't swap Venice for the Cinque Terre.

If you absolutely want the Cinque Terre, see if you can add 2 nights to your trip. This would be the sequence:
VENICE: 3 nights
FLORENCE: 3 nights
CINQUE TERRE: 2 nights (or at the very least 1 night)
ROME: 4 nights (or at the very least 3 nights).

Travel is still by train.

I can add a testimony: I followed Roberto's recommended itinerary above and it was perfect. Fly into Venice and out of Rome. Savor the three cities.
Cynthia

Just as a point of clarity: train to time from Florence to Venice is shorter than train time from Florence to the Cinque Terre, though neither trip is onerous.

Add as much time to your trip as you can. There's no shortage of wonderful things to see and wonderful places to go.

Thanks for great info. Does it make any sense to do a day trip to CT from Florence?

I agree with:
VENICE: 3 nights
FLORENCE: 3 nights
ROME: 4 nights

I have been to Italy four times (not counting cruise ship stops which would make five), most recently a few months ago. Definitely fly into Venice and out of Rome. Venice airport is not that accessible from the city center, and flights home tend to be really early.

I might consider heading to Florence on a later train, because Venice is a place that you might not make it back to as often--it's not on the way to anywhere else. Plus, hotels are extra expensive in Venice.

Cinque Terre was nice when my wife and I visited in 2007, but from what I have read on this board it's not worth going out of your way for anymore (sad). As Yogi Berra supposedly said, "nobody goes there anymore, it's too crowded". If you really want do a day trip from Florence, Sienna or Lucca would be good ones. But three nights in Florence is actually not much. I spent four nights there on my recent trip and it was not enough.

Trains between these cities are really easy, might want to book ahead though.

"does it make sense to day trip to CT from Florence". Others may disagree, but I would say no. You will spend too much time in transit. Cinque Terre is wonderful but so are a lot of other places in Italy that you're bypassing - you really have to embrace that you can't see it all in 10 days (10 months or 10 years)! I agree with Venice 3 - Florence 3 Rome 4. Great trip!

I agree with Venice, Florence, Rome. It is a real pain to get to the airport in Venice for an early morning departure. Skip CT until another trip. Remove a day from Rome and add to Venice.