15 Night Italy Trip

How many nights - and days - do you actually have there - not including your travel dates?

It's generally not smart to book flights until you have at least a rough itinerary (and sequence) figured out. Because...well, where are your flights in and out of? Hopefully in to Venice and out of Rome? A logical sequence depends 100% on that.

Just a guess, but you may need to drop one of these planned stops, as you may be unrealistic about how much usable time you actually have in each...since you consume some/most of a day each time you pick up and move yourself. Remember, "X nights" in any place results in "X-1 days" to spend there. Once you subtract 1 from each of your proposed stops (eg 1 day in Venice) the real impact of this starts to hit home. Start by being honest about how much time you actually have there, and how long it takes to "move". Worry about "must see" items later.

Cinque Terre is probably better placed after Florence, before Amalfi.
Since your time is limited and you are already including the Amalfi Coast in your itinerary, you might want to consider eliminating the Cinque Terre from this trip.
You could allocate those two nights to the rest. Venice for example deserves 3 nights, and the Naples area (Amalfi) could certainly benefit from a fourth night.
Alternatively you could eliminate Amalfi and stick to the Cinque Terre instead.
Frankly if someone gave me a choice between Cinque Terre and Amalfi Coast, I would go for the latter, unless I had only a couple of nights. The Cinque Terre can be seen in one day, but the Naples area has so much to offer (Amalfi, Positano, Ravello, Sorrento, Capri, Pompeii, Herculaneum, Ischia, Procida, Naples, etc.). You could spend over a week there and not cover half of what you could see.

i would add one more night in Venice and one more in Rome and skip CT. Amalfi coast will give you your 'coastal' experience and one less move will make your vacation much more enjoyable overall.

Venice-Florence-Amalfi-Rome , assuming your flights are into Venice and out from Rome

15 days is not much time...really. If you could add a week your plan could work.
I would eliminate Amalfi and save it for a different trip..a trip more focused on that end of Italy, flying in to Naples.
Without Amalfi I would add one night to Venice, keep CT, and add two nights to Rome. I would plan to visit Sienna from Florence (bus from the train station) and Orvieto (by train) from Rome.
From my experience it is better to plan multiple trips to Italy that focus a bit more on the regions than try to skip all over the place. It is possible to do as you plan, but it will be rushed and you will be pushing too hard to enjoy the areas you are in.

I also think this plan is too rushed. As David pointed out, you'll spend big chunks of time getting from place to place. Two nights in Venice means only one full day there, plus whatever partial jet-lagged day you have on arrival. I'd give Venice more time at the expense of Cinque Terre and/or Amalfi. And I hope you booked "open jaw" into Venice and out of Rome.

I haven't been to CT or Amalfi but I'd pay attention to those who recommend choosing one or the other to reduce your moving-around time and get a better coastal experience.

For "must sees," see the "Explore Europe" link on this website, and click to Italy and the cities/areas you choose. While everyone's priorities may be different, our host's selections are usually very good.

Count me among those recommending one coastal experience instead of two.

joe32f has the right idea.

You will have a lot of travel time getting to and from the Cinque Terre as well as to the Amalfi Coast. Did stances seem short but the time it takes is significant. Best to drop the CT.

Venice deserves more time, it’s not the most convenient city to get to and it’s not on the way to as many other places, so you may be unlikely to be back soon. Check travel time on Rome2rio. I agree with dropping CT or Amalfi. If you only go to Amalfi Coast on the southern leg you are missing a lot that’s in between, as someone pointed out. By covering so much ground you are risking having a too short and unsatisfactory visit to each stop.

joe32f has the right idea. You will have a lot of travel time getting
to and from the Cinque Terre as well as to the Amalfi Coast. Did
stances seem short but the time it takes is significant. Best to drop
the CT.

Ditto! Drop the CT and use those days elsewhere. 4 nights on the Amalfi might be a better idea given the time it take to get there.

I've been to all and strongly agree with suggestions to drop the CT. I'd probably add a night to Venice and then Amalfi or Rome.

Please keep in mind that it's a 5-7 hour trip from Venice to the CT. Which would only give 1 day there. Is it really worth it?

I should add...the order of travel should change to minimize travel time. I would travel from Venice to Florence, visit Sienna from Florence by bus, then travel to CT. From CT I would head to Rome. .
In Rome you might (should) consider Ostea Antica and possibly Orvietto as day trips....or you could visit Orvietto on the way to Rome. As noted in my earlier post, add days to Rome by dropping Amalfi.