First time visitor to Rome

I suggest you stay in the Piazza Navona/Pantheon area, where you are within easy walking distance of numerous sites including the market at Campo dei Fiori, the "French Church" with its Caravaggio paintings, and at that time of year, the Christmas market in Piazza Navona. You're also reasonably close to the Vatican, by foot or taxi. Just strolling around, aside from your Vatican tour, there is lots to see and many food choices too. The Christmas lights should be up right around this time, illuminating the side streets as well as the big squares. Rome is beautiful in December. In my opinion you don't need a golf cart tour as it won't be hot and pedestrians rule this area.

Check out Eating Europe for food tours. I’ve taken four and have two more scheduled for September, Rome and Florence. Have not been disappointed in any of them.

Stay near the Pantheon (we loved Alberto del Senato), do a Colosseum tour in the morning, then spend the afternoon on your own exploring—Spanish’s steps, Trevi fountain. There was also a beautiful church we stumbled upon (St. Ignazzio of Loyola?). Have lunch at Antica Salumeria in Pantheon square to enjoy a charcuterie platter and wine. Dinner in Piazza Nova at Bernini Ristorante (another Rick recommendation).

Since you didn't indicate a huge interest in the Colosseum so you might be satisfied with just a look at the outside?

I love ponygirl813's description of Rome at Christmas time- makes me want to be there at that time!

You don't have a lot of time. Stay right in the center- near Pantheon/Piazza Navonna or Campo de'Fiori.

A golf cart tour might be just right- if that is what you need. Are there mobility issues?
If you don't have any mobility issues-walk to the Colosseum. See the outside, go to the viewpoint behind Capitoline Museum to see the Forum. You can walk home from there.

Rome is more compact than it seems.

A food tour would also be great- most are in the evening now
Try Eating Europe - always gets high marks here. We loved our tour in 2019.

Or just enjoy the holiday ambience on your own- do RS Heart of Rome walk in the evening.

Lots of people will be out strolling.

Tuesday am take a taxi to the Vatican, visit St. Peter's- walk home- visit a few churches, markets and the Pantheon.
This evening enjoy apertivo and dinner on Piazza Navonna.

Hoping for good weather!

Eating Europe’s Twilight Trastavere food tour would be a perfect fit for Monday night. Kudos on getting that early ticket for Vatican Museums, you’re going to feel pretty smart walking past the queues.

Vatican Museums are a big sight, I wouldn’t plan too much for after. I would taxi to Campo d’Fiori for lunch, then do a “Heart of Rome” walk from there to Spanish Steps and Piazza de Popolo. There’s an incredible amount of churches, the Pantheon, and just great “Rome!” ambience to be had. You can walk this at your leisure and nope out anywhere.

Heading up to Palatine Hill and just seeing the Forum and Colosseum from there is pretty awesome. It’s worthwhile even if you don’t go inside the Forum or Colosseum itself. In fact, I’m firmly in the “don’t bother going inside the Colosseum” camp.

Everyone has their preferences but we prefer to stay in the Termini area in the Hotel Sonya, across from the Opera House. Good area for access to transit and restaurants. You will take the train from the cruise port and you can walk to your hotel in the area. A high percentage of buses, trams, route through Termini so if you can easily catch a bus or tram back to Termini after a long day of wandering in the rest of Rome.

Thanks to everyone for the helpful insights and advice!