Early Dec: Florence, Rome, Sorrento?

Florence Rome Sorrento is too much for only 6 days.
Just do Rome and the Amalfi coast since they are closer and "you really want to go to the Amalfi Coast" and you shouldn't go by what everyone says about Florence. I don't think it will be too cold to hike as long as you are moving; everyone has different threshold. I have been to Italy 3 times in the winter including December 2015 and 2016 and it is mild by Chicago standards.

Arrive Rome go straight to Sorrento and spend 3 nights.
Train back to Rome stay 3 nights. You can do Florence as a day trip of you feel like it.

You could go to Pompeii on the way back to Rome. There is bag storage at Pompeii.

I would do Florence 3 nights and Rome 3 nights.

The idea of doing the trip Florence-Naples, then visiting Pompei, then going onward to Sorrento in a single (winter) day is stretching imagination really too much. In 6 days you can visit two places. Personally I would prefer to visit two cities as, being winter, if the weather is not good you would have more things to do in a city, but that is your choice.

Rome and one other destination is all you have time for.

Do Rome last so you are in position for your flight home.

Check sunrise/sunset times for your hiking days. You will be there for some of the shortest daylight hours of the year

Drop Florence. I've been 9 days in Rome & only 1 museum (+ 3 palace/museums where I go for the palace).
Pompeii + hiking on Vesuvius might be an option instead of Sorento ( including 1/2 day Naples & half day Herculaneum)

Your problem is going to be risking the weather for the one day you're allocating for hiking the A.C. coast. Cold temps probably won't be an issue but rain could be, and there's not a lot to do in the that region if it's not nice enough to be outside. Also consider that aside from Naples, Capri and some other islands, ferries won't be running from Sorrento to other coastal locations, such as Positano, at that time of year (although SITA buses will be).

That said, if you reduce your trip to just Rome and the A.C. you might increase your dry-day chances. Should the weather cooperate, there is some fun hiking on Capri as well (been there, done that). A lot of businesses on the island will be closed for winter but that doesn't affect the ability to do some hoofing about.

Rain? You'll have to get creative.

I love Florence but I'm also a museum/art/architecture geek so if not into that stuff, you might not enjoy it.

So, I'd opt for just the A.C. and Rome. Do look at hiking (more like walking, really, as it's flat) some of the Appia Antica? We've done quite a large section of it and voted it our best day in Rome to date: lots of interesting things to see along the way, and the further out you are on it, the more non-urban the countryside. It can be biked as well.

https://www.parcoappiaantica.it

Florence is a “must” only if you think it is. If you are not into museums and have so little time, it does not seem to make sense for you.

We have been to Sorrento in December and were fortunate to have cool, clear weather. Pompeii was not crowded nor were the buses to Amalfi. Hiking is tough by public transportation but Rick Steves points some out in his guidebook including a nice walk from Amalfi town to Atrani that we enjoyed.

I agree with Kathy ‘s recommendation to consider the Appian Way while in Rome.

Cut your travel to two places. Six days is enough for Rome, but you can stretch it to do Florence.

Really good post from Laurel. Put your home city in your profile so we can see how long the flight is for your six-day trip. Did either of you study Art History? (I ask to determine whether to drop Florence or Sorrento.) Do you know Sorrento is 54-62F with 15 days of rain in December? (I've only been there in the summer.) In season, Sorrento books up six months in advance. Sorrento has only one single, squalid (OPINION) beach, beside the commercial marina.

Just emphasizing what others have already said.

In 6 days you cannot do it all, and you can't even do what you've proposed, unless you want your only memory of the trip to be moving from place to place.

Florence is only a must if it is a must for you. Otherwise, use your limited time to see places that interest you more. Particularly since you say museum days are not appealing, and these are a big part of Florence (although of course not the only thing). Be sure you find something that does appeal to you about Florence before you commit to nights there.

If you like exploring, you may do best to spend all your time in Rome. It's one of those places where most of the tourists are focused on a very few places (such as the Colosseum and the Vatican Museums). By going elsewhere, it's just you and the Romans; recent reports indicate that many other churches and museums are still sparsely visited, even in high season. I love just walking around Rome, popping into any church that I pass. If that sounds appealing, you'll have a great time in Rome.

Similarly, Naples is little touristed, but it is a very intense place. All sightseeing in Naples is like urban exploration; if that sounds good to you, look into it.

Thank you everyone for your feedback and advice!! This was exactly what I needed to hear! I’m cutting out Florence and splitting the trip as recommended. I’m overwhelmed by the positive and honest recommendations! If anyone has any other specific to-do’s (I loved the Appian Way recco!), please feel free to share!!