Rome Nov 24 to 30 RS tour single lady

Since it's assumed you would have to be in Rome for the last night, going somewhere for three nights would yield two full days in that location. Possibly best to stay in Rome and add some day trips. Naples by train [e.g.] is seventy minutes.

When we did this tour some years ago, we ended up staying an additional 9 days in Rome, and never ran out of things to do. It's a great tour; you'll have a good time and learn a lot.

Maybe a day trip to Pompeii, but stay based in Rome?

If those destinations are on your bucket list and you won't be back to Italy soon, I say go for it. As pointed out above you wouldn't really have 4 days in the Naples/Amalfi Coast area, as you wouldn't arrive until Saturday afternoon earliest and you'd have to return to Rome by Tuesday afternoon or early evening latest. Even so, you would have time to see the places you mention in your post. Sorrento will likely still be somewhat active at the beginning of December and with lower hotel prices, so it could be a good base. It would be difficult to fit in a Tivoli tour unless you return to Rome on Monday evening, and that would make the time in Naples/Amalfi Coast area very rushed. I don't think trying to do a Naples, Pompeii and Amalfi Coast day trip from Rome is practical. You'd need to cut out Amalfi Coast and even then it would be a long day trip.

Edit: I did Sorrento for 3-4 days prior to a Rome tour several years ago and it worked very well. Doing it after won't be as efficient, but it would work.

The train to Naples is incredibly easy, but note that the transfer to Pompeii is more complicated, must change stations in Naples. Once you get over to the Circumvesusia train, the Pompeii Scavi station is right at the main gate. Keep in mind, your station is Pompeii Scavi, not Pompeii.

"The train to Naples is incredibly easy, but note that the transfer to Pompeii is more complicated, must change stations in Naples."

Technically that's true, but the two stations are within one complex - you don't even have to go outside. You just go from the Trenitalia or Italo section to the Circumvesuviana section downstairs. If I hadn't known in advance, I wouldn't even have thought it was a separate station.

The downstairs station is Garibaldi; here is the schedule

https://www.sorrentoinsider.com/en/naples-to-sorrento-train-schedule

You can store your bags in the main station [deposito bagagli].