16 days itinerary in Italy

Looks pretty good.
I'd try to give Venice 3 nights.

Train from Florence to Salerno- then ferry to Amalfi will be your easiest route - (avoids the longer more complicated route Naples- Sorrento- Amalfi)
Then train from Salerno to Rome.

Any interest in Pompeii?

I assume Cave Blue is Blue Grotto- don't waste your time.
We really enjoyed our boat trip around the island of Capri though- you will see a lot more interesting rock formations and other grottoes without the hassle/expense/wait at Blue Grotto.

I agree with Christine that an extra night in Venice would be good. I also think that your time on the AC is very packed. And remember that it could take you 5-6 hours to get from Florence to your AC hotel on your first day. You may find that you have to omit something. That would likely be Capri, since it would require the better part of a day all by itself.

Are you thinking of doing one day trip in Florence covering both Pisa and Siena? If so, I don't think you'd experience much of those cities. Budget friendly suggestions:
Florence--We really like Hotel Il Bargellino. Huge room, nice location next to the train station, super clean.
Sorrento-La Magnolia BnB. Nice included breakfast, nice sized room, great location just off main plaza, super clean
Rome--Hotel Contilia, by the train station, clean, huge breakfast. This is a safe area, and convenient to transportation. It is not as good as other locations, but it is very budget friendly and with the metro and buses its easy to get everywhere. It also is within reasonable walking distance to many sites.

I would save the AC got another trip. Add more nights to Venice and stay in Tuscan countryside in addition to Florence. Your plan seems too rushed to enjoy the places you want to visit.

Budget friendly? Price? Means different things to each person.

Florence. Hotel Annalena, in the Santo Spirito neighborhood.

Sorrento. Hotel Il Nido. Up in the hills, views overlooking the town, the Bay of Naples and Vesuvio.

Great staff, wonderful food, shuttle into town or a 20 minute walk downhill.

Rome. Hotel Villa San Pio. Aventine Hill area. Gorgeous gardens, wonderful facility, central, in a quiet area, easy access to transport by metro and bus.

Agree with others, if possible add a night to Venice.

It would help to know what your interests are.

Allow enough time for travel. What is lunch time? If you land in Venice at noon, you probably won't be at your hotel until around 2. Try to stay awake until it's late enough for an early supper and try to get a good night's sleep. Then you have one (hopefully not too jetlagged) day for Venice. I agree it deserves at least 2 full days. You'll use much of the morning going to Florence. Though it's about 2 hours on the train, you'll need time to pack and get to the train, then time to get to your new hotel and check in. Have lunch and you've got about 1/2 day. Then 3 full days, one for Florence, one for Pisa (you only need 1/2 day) and one for Siena. If you plan to stay in one of the towns you mention, it will take you the better part of a day to get there and another to get to Rome. That gives you 3 full days in Rome. Day 16, if your flight is at noon, you need to leave your hotel around 8 am to get to the airport by 9 (3 hours pre-flight). That means probably packing the night before.

Add some down time. Changing locations is stressful - packing/unpacking, getting oriented to new room, new transportation system, new area. You will need time for laundry and shopping for incidentals/toiletries. Summer is hot and crowded, expect to spend some time standing in line, whether it's to buy tickets, to enter a sight, or to wait for a bus or ferry. Your itinerary, with the exception of Rome, sounds like you plan to go somewhere by train/bus/ferry nearly every day. If you've traveled that way before in Europe and are comfortable with it, great. But if this is your first visit, it may be too much go-go-go and you may find that by the time you get to the AC, you really need some slow time. Standing in line for crowded buses and ferries may not appeal. I go back to my original question. What are your interests?

Do you want a room for 3?

Budget friendly at the height of tourist season isn’t very doable particularly on the Amalfi Coast. Consider a few more days in Venice with day trips to Padua, Vicenza, Verona and/or Treviso. Add another day or two to Florence, possibly a visit to San Gimignano. Plan on some day trips from Rome - Orvieto, Tivoli, Ostia Antica.

The Amalfi coast is beautiful but in summertime it can be as crowded and frustrating as Disney World. Prices are at their peak and transportation is hellish because of narrow roads and a plethora of tour buses. The heat can become unbearable. Spend more time up north and save Amalfi for an off-season visit.

Consider staying at Sorrento near Amalfi Coast. We loved the Blue Grotto with our boatman singing "O sola mia."

Florence, check out the Hotel Balesteri on the Arno, great location.

I also think you should give Venice a bit more time so you can visit the outer islands (great way to escape the crowds). I would also recommend an apartment versus a hotel... For a unique experience, take the water bus from the airport to the inner lagoon - it's a bit pricey (~€15pp) but worth at least it once.

I would also get an apartment in Florence since you're going to be there a number of days. There are plenty of affordable 2 bedroom apartments within walking distance to the main train station. I would plan on taking the earliest regional train you can to get to Pisa. If you leave early, you can beat the crushing motor coach crowds. (The tourist crowd I experienced in Pisa was the worst I've ever seen - I've never been pushed, shoved and hit with selfie-sticks so much!) I would then catch the train to Lucca for an enjoyable afternoon walking or bike-riding the wall before heading back to Florence.

Thanks everyone for the suggestion. I have edited our itinerary.

Day 16: Naples
Day 17: Fly to home

Presumably, this means flying out of Naples?