Itinerary

Are you missing anything? Well of course you are. You can't spend a month in Italy and hope to see everything. As it is your itinerary is too ambitious IMO, given the distances you want to travel. While I haven't been that far south, I've read many forum members say that Sicily needs at least 2 weeks of its own. If you omit Sicily and add an extra day to some of your cities (you're going to need to do laundry at least a couple of times, and for sure you will need at least 1 vacation from your vacation at the pace you're setting), then I think you'll have a more enjoyable, less hectic trip.

How wonderful that you'll have 29 days in Italy!! You'll have time to visit a lot of places, though perhaps not everywhere you've listed.

I suggest you start with a very rough plan of the number of days/nights you want in each of your cities. Something like what I've done below, based on your input. You'll see that I've included all of your named cities, which - by the time you add travel time - adds up to well more than 29 days. You'll need to begin to prioritize.

Once you've narrowed down your top cities, you can map out a sensible route. You'll also need to allow about a half a day of travel for each move: allowing time for train and transit to/from hotels.

Arrive April 23: travel to Florence (assumes an early arrival in Rome)
5 Nights Florence: 2 day trips (note, I've added 2 nights in Florence to give you time for sightseeing there!)
2 Nights Siena: 1 day sightseeing Siena
3 Nights Cinque Terre: 2 days sightseeing CT
4 Nights Venice: 2 days sightseeing Venice, 1 day islands
4 Nights Bologna: 2 days Bologna, 1 day trip, fly to Catania
10 Nights Sicily: 9 days Sicily, pick 2 or 3 cities as bases (fly back to Naples)
- either stay on east side of Sicily and fly back out of Catania, or visit Palermo side and fly back from there
3 Nights Naples: 2 nights sightseeing Naples
4 Nights Amalfi Coast: 3 days sightseeing Amalfi Coast
5 Nights Rome: 2 days sightseeing Rome, 2 day trips

Fly home from Rome

Hi Sharon, and welcome to the forum. A few questions first.

Are you flying R/T in and out of Rome? Have you booked any lodgings yet? Why is Sicily important to visit?

Answering these will enable us to help you complete a your itinerary with less backtracking.

You have plenty of locations as is, but pick one or two that you'd be willing to eliminate.

Yes we fly into and out of Rome

Sicily is on the bottom of my places to visit.
So far we have booked an apartment in Rome, Trastervarre area, and an apartment in Florence.

We have been to Bologna, its OK, but I don't rate it high enough to recommend spending time there. Nearby Ravenna was worth a stop.
Umbria should be considered. Take a look at Perugia, Spoleto, Assisi and Orvieto. Also, Lucca and Pisa.

Given all your other proposed destinations, I would drop Sicily and plan to see it on a later trip. I loved it, but it really needs at least 2 weeks, and that's with a car. Three weeks would be better.

On two trips totaling 29 days on the ground, we have seen everything on your list except for Bologna and Sicily. If you omit Sicily as suggested by others, you can add more time to Florence, as suggested by CWSocial, and you can add to Siena or other location in Tuscany.

I'd suggest tweaking something like this based on your interests. I left out Bologna as we haven't been there and others suggest it isn't as high priority, but you could fit it in by cutting 2 nights elsewhere.
3 nights CT (or even just 2)
3 nights Venice
5 nights Florence if you want to do day trips, 3 nights is barely enough if you only want to see the highlights in Florence
4 nights Siena or other Tuscan location such as Montepulciano
3 nights Naples (although we only had 2 nights, there is more to see, as long as you don't mind this very intense city)
1 night Pompeii on the way to Amalfi Coast if this interests you. We don't usually do one night stops but it worked great for getting up and into Pompeii early and then leaving for Amalfi coast mid-afternoon after a late lunch.
4 nights Amalfi Coast
6 nights Rome

Enjoy your planning!

This itinerary might avoid unnecessary backtracking keeping most transfers under 2 1/2 hours.

Rome. 5 nights.

Train to Naples 1:17. Circumvesuvian to Sorrento? Or Private driver to Amalfi Coast 1:06-1:20 hrs.

Amalfi Coast. 4 nights

AC-Naples same as above train/driver. 3 nights.

Naples-Venice. Train. 3:45. 4 nights Venice.

Venice-Bologna. Train 2:00 3 nights

Bologna-Siena. Bus. 2:30. 2 nights.

Siena-Florence. Bus. 1:17. 4 nights.

Florence- Cinque Terre. Train 2:27 3 nights.

Cinque Terre-Rome. Train. 3:45. 1 night.

Edited to add a few clarifications.

Thank you everyone very much for all of your advice.

We're getting closer to our Italy trip and so fair this is what we have decided. I'm sure there are pros and cons with this itinerary. But it is what it is......We've booked Airbnb apartments for our trip. My only true concern is the trains, buying tickets for each train or a Euro pass. I'm leaning toward the Euro pass if I can figure out how they work.
Tuesday April 23 arrive in Rome 23-28
April 28- May 1 Florence
May 1-4 Siena
May 4-7 Cinque Terre (Riomaggiore)
May 7-9 Bologna
May 9-13 Venice
May 13-17 Vico Equense - near Sorrento
We will be taking day trips and planning a private tour of the AC, Capri, and a day in Naples. We will of course visit Pompeii.
We did take Sicily off feeling it was too much and too big of an area to cover on this trip.
We have a few tours booked in different areas including wine tastings and such. Can't wait.
We have to figure out what we're doing with our last few days. We fly out of Rome on May 21.
Any advice is more than welcome.

For great advice regarding train travel in Italy, use the website www.seat61.com. You will likely save money by purchasing individual tickets, not a rail pass! If you are willing to commit to specific trains/times for the Rome-Florence and Bologna-Venice trips, you can save quite a bit purchasing non-refundable advance saver tickets from Trenitalia or Italo. It takes a little extra time and planning-just remember that it will pay off in extra Euros left over for more gelato:)!

Den, thank you on the train advice. That’s my next step to figure out......we are considering a flight from Venice to Naples. The airfare is less than train! Shocking!

Yes Pompeii is top on our must see list.
Thanks so much.