First time in Italy - 8 to 9 days

With this amount of time I would do Florence and Rome and visit Ostia Antica in Rome for a 2000 year old Roman town. If it must be Pompeii and I understand the appeal, do a long day trip from Rome. YOu don't have time to do justice rome and Florence and also spend substantial time in Sorrento Capri etc.

U could try this, but as others will say, more time would be preferable ... (I'm gonna work on 9 nights)

Day 1 - Arrive Rome. Direct to Sorrento - 3 nts
Day 2 - Day to Capri
Day 3 - Day to Pompeii (& Naples/Herculaneum)
Day 4 - Train (via Naples+Rome) to Florence - 3 nights
Day 5 - Florence sights (BOOK if planning Academy or Uffizi)
Day 6 - Day to Siena
Day 7 - Morning to Pisa. Afternoon train to Rome - 3 nights
Day 8 - Rome sights - Colosseum, Forum, Trevi Fountain, Spanish Steps
Day 9 - Rome sights - St Peters, Vatican, Pantheon, Piazza Navona
Day 10 - Depart Rome

First, don't underestimate how long it takes to go from place to place (packing/unpacking, getting to/from train stations in city traffic, checking in/out, etc). Second, with your very limited time, you should plan well to maximize your "enjoyment" time.

It's easier to day trip to Pompeii from Rome than to shlep to Sorrento and back with all your belongings. And Ostia Antica is very interesting with some similar features to Pompeii and it's an easy half day trip from Rome. From Florence you can day trip to Siena one day and to Lucca and Pisa on another. From Rome, day trip to Orvieto. Each has its own character, quite different from each other.

So I'd fly in/out of Rome, start with a few nights in Florence and the rest in Rome. There's so much to see in and around both of these great cities. As you wrote, this is your first trip. You will be back!

Chani's first sentence contains good information / advice that most people never consider until it's too late. You want memories of places, people, good food and wine -- not just memories of train stations and hotel lobbies.

To the Op: first you mention Florence and Rome which sounds like a perfect plan for your days.
But then you start going far south of Rome to an entirely other region.

If you want to day trip from one day in Rome as far south as Pompeii, that is fine. A longish day but many do it, some prefer
Ostia Antica for a similar experience to Pompeii that is much closer and easier to reach from Rome for that day trip instead.

Naples/Sorrento/Capri/Amalfi Coast I would consider a separate destination, they are not Rome day trip options and ones unless you want to drop Rome or Florence that you DO NOT have time for on this trip.

If you only have 8 nights, I would try to stick with 2 main bases.

Don't forget it basically takes a day to get there, so your 8-9 days become 7-8 days.

What do you love? Ancient/medieval history = Rome, Herculaneum, Pompeii, Ostia Antica, Hadrian's Villa, Tivoli
Renaissance == Florence = Art, architecture, Siena, Lucca, Pisa
Romance = Venice

Anywhere you go in Italy you will art, history, local culture and food and wine. Pick your pleasure.

Thank you everyone for your advice! We booked our flights to/from Rome so now its officially planning time! I really appreciate all the details included in your responses and will definitely take them into account.

I do have one more question... any suggestions on what area of Rome and Florence to stay at in terms of getting around with public transportation? Also, how are taxi's in Rome & Florence - cash only? reliable? scammers? Thanks again!

For Florence, I recommend staying in the center of town near the Duomo (within a few blocks). Florence is a very walkable city so you may not need to use public transportation at all. Take a look at booking.com or vrbo.com for options in all price ranges. For Rome, I like either Trastavere (across the Tiber River from most sights) or the Campo de Fieri/Pantheon area. In Trastavere, there are many tram and bus lines to get you around town. In the Campo/Pantheon area, you can walk to a lot of sights plus Piazza Venezia and Largo Argentina are big transportation hubs. As for taxis, I have never had any issues, but there is a section on using Roman taxis in the Rick Steves Italy guidebook.

The only reason to take a bus in Florence is to go up to Piazzale Michelangelo (for the view) or to Fiesole (for the the view and the town). A good bit of the center is closed to motor vehicles and everything is close to everything, including the train station (Santa Maria Novella, aka SMN).

Rome is more spread out. If you are planning day trips, you should plan to be either not far - but not too close either - from Termini (train station) or near a metro stop. I think Trastevere is a little remote for a first visit. I've found it better to be near a metro stop anyway, because there's so much walking in Rome, sometimes it's nice to have that option.

I've only hailed cabs a couple of times on the street, no problem, nor when my hotels ordered taxis for me. Just be careful at Termini itself. The official taxi rank is in front of the station and you can trust them. I believe there's also one on the side, but there are also a lot of less-than-honest drivers there who will try to con you into a highly overpriced ride.

Chani was very lucky to hail cabs in the street (I have done it a few times, too). Taxis in Roma don't cruise, they usually are in their way to a fare if they are empty. Taxi stands are found at every major sight, however, and your hotel can call one for you or reserve one ahead of time.