I visited Rome in 1994 and 2022.
I recommend the Hotel Lancelot: https://www.lancelothotel.com/. It's close to the Colosseum and has ensuite bathrooms. Though it offers breakfast and has a lobby, I would not call it a fancy place.
I also stayed at the CF Laurina: https://www.residenzanobilelaurina.com/en. It's on Via Laurina right off the Via del Corso, the main street of Rome, and not for from the Piazza del Populo, a famed square that houses an Egyptian obelisk.
You could tour some of the breathtaking churches in Rome's center. I saw the Basilica di Santa Maria Maggiore, San Giovanni in Laterano (the first Vatican), Santa Maria in Trastevere, Santa Prassede & San Zeno Chapel, the Basilica of San Clemente and San Pietro in Vincoli (with its famed statue of Moses by Micheangelo).
Santa Prassede & San Zeno Chapel deserves a bit more notice because it for me was the most amazing church. On the outside, it's nothing special and, in fact, a bit bland. Inside is where the show is. The mosaics are the best in Rome. It's a late Roman church. The Romans had seemingly lost the ability to mosaic grand churches and "imported" artisans from Constantinople. Artists there had learned from the Romans and gone beyond them. So when Rome called to mosaic a new church, it was like a returning faith.
San Clemente is renowned for its "lasagna" of history, with at least three distinct layers of architecture and activity built one on top of the other, spanning nearly two millennia. Visitors can descend from the 12th-century church into a 4th-century Christian basilica, and further down into a Roman building complex that includes a 1st-century house and a 2nd-century temple to the god Mithras. It's underground complex offers a rare, physical journey through Rome's evolving history, including a mint.
The Appian Way is an excellent walk or bicycle ride. It's like walking through history with the monuments, ancient structures and aqueducts. I walked the Appian to Aqueduct Park (https://www.romesightseeing.net/aqueduct-park/). If you bicycle the Appian, be extra careful: I saw a woman who had tumbled from her bicycle. You would be bicycling over 2,000-year-old pavement.
Also, the Christian catacombs of Rome (https://www.catacombesancallisto.it/en/index.php) will likely be open on Sunday. And they're near the Appian Way. You will see the tombs of nine early popes in these catacombs.
