rome sights

There is so much to see in Rome. I have been twice and still did not see anywhere close to all of it. That said, a few thoughts: The church of St. Peter in Chains has a fine statue of Moses to see. The Catholic Church does not have an official position on if the chains are the actual ones used on St Peter, but you can still see them anyway.
I did also get a kick out of Gariboldi's blue jeans in the museum of the Risorgimento (open every day except a few holidays, if I read the sign right), if you are looking for something a bit out of the ordinary run of touristy stuff. IF they are genuine Levis, then the company should use them in every ad in Italy until the end of time. :)
There is also a nearby museum in the Victoria Emanuelle II monument that has displays in Italian on the experience of emigrants from Italy. My limited Italian was barely enough to grasp the essential parts of what each display was trying to convey. If your Italian is better, you will get more, I'm sure.
Just to walk around and know what you are seeing is history was a big deal to me. The Trastevere neighborhood has some good food. Also, a funny story. My nephew was on a different tour of Rome, and noticed that the manhole covers say SPQR and decided that must be the foundry that forged them. :) If you are not familiar with the Roman Republic, that is the abbreviation for the Latin phrase which translates to the Senate and People of Rome.
The Bourghesi Gallery was also good to see.
A few of us on one tour went to the Eutruscan museum and enjoyed it.
The Rome City Museum was also of interest to me. One of my favorite stories is the guard and I sharing a laugh about our limited knowledge of each other's language.
Anyway, the best advice I can think of is to figure out what interests you most, art, architecture, history, or just being in a foreign city. Then look up in a guidebook things that fit that bill.

The Colosseum, Forum and Palatine hill. We took a walking tour of the Forum and learned so much. The Pantheon is pretty incredible.

San Clemente church has a long history that can be seen by walking down to the basement, and then go down further until you realize you are walking through the original streets of Rome, fascinating. The church is worth visiting for itself, quite small and very beautiful. It’s only a short walk from the church to the colosseum and on to the Forum.

Ostia Antica, an easy train journey from Rome, was the original port of Ancient Rome; it was abandoned when the river silted up. The ruins are extensive and can be compared to Pompeii but without the dramatic story and sudden demise. Still fascinating and not crowded.

The Ghetto area, with its reminders of the round-up of Jews in 1943, Kosher restaurants and the magnificent Synagogue.

RS Rome guide is a good source of walks around areas of Rome.

A good guidebook, like Rick’s, will provide all sorts of ideas for what to see in Rome. You can see what appeals to you.

John, did you ever take the tour suggested to you a few years back (you apparently had 4 days to work with that time.)

https://community.ricksteves.com/travel-forum/italy/tour-guide-for-4-days-in-rome

If not interested in a tour, what sorts of things are you interested in seeing/doing?

I second travel4fun's recommendations above.

Walk the Roman Forum and visit Palatine Hill. Go visit the ancient Pantheon and afterwards stop in nearby San Luigi de Francesi Church to see the Caravaggio paintings there. Have lunch in Monti neighborhood near the Colosseum.

https://www.ricksteves.com/europe/italy/rome

Purchase Rick Steves Pocket Rome guidebook and take his Heart of Rome walking tour. You can download an electronic version from his app.