Rome cruise 10 day

Welcome to the forum!

Do you have guide books for Rome and Athens?

If not you can start here
https://www.ricksteves.com/europe

I'm so glad that you are planning extra time on either end of your cruise, especially extra time in Rome.

When I am trying to determine what sights might interest me in a particular location, I will often head to you tube where there will be a plethora of videos labeled along the lines of "top sights in Rome", "Athens top ten" etc. This will help give you some ideas.

I would also head to your local library and look in the travel section for guidebooks on Rome and Athens. No need to buy a guidebook if you are really just looking for ideas and information. Always double check any information from a guidebook with the website on the internet in case there are updates or changes.

Finally, unless you really need kitchen facilities for your short stays, I would look at hotels vs. Air BnB's. Having a hotel front desk to handle questions is very helpful in a new location. They can call taxis etc for you and give you some assistance.

I'm ending a cruise in Athens in October. I chose to stay 3 extra nights. It could have been more, but at that point I will have already been gone from home over 3 weeks and I know that I will be feeling like I am ready to go home. My focus is on the Acropolis Areas and museum, and a 1/2 day trip to ancient Corinth. I figured out what interested me and that is what I planned for.

I know that you will have a great trip. Be sure to come back to forum and tell us how it worked out and anything you discovered that might be helpful to the rest of us fellow travelers.

Athens,
Of course, visit the Acropolis and the amazing Parthenon. Be sure to visit the new Acropolis Museum, which is on your way up the hill to the Acropolis. Also, recommend the Museum of Archaeology and the changing of the guard.
https://realgreekexperiences.com/athens-changing-of-the-guards

There are other ancient sites within the city, some Greek some Roman. Also, the Temple of Poseidon a bit south of Athens is interesting. Nearby Corinth and the canal is with a half day. Also, consider taking a three island half day cruise from Piraeus port.

Rome,
Many great things to see there here are some.
The Forum and Coliseum. Also, try to visit Nero's old palace nearby.
The Capitoline Museum nearby; The Pantheon, Spanish Steps, Hadrian's Mausoleum, and Trajan's column.
Most importantly, St. Peter's Bascilica and the Sistine Chapel.

Since you are on the RS forums I would get a RS guidebook for Rome and/or Athens.