We'll stay in Rome for 4 nights, flying out on the last night from Rome's airport back to the US. Hoping to stay near a train station in the city or any place you would return to. We are in our 70s and will not have a car. Will walk and take public transportation, etc. This will be our 3rd visit to Rome, so have seen the major sites. This time, we'll take our time exploring out-of-the-way places that we have yet to see. If you have suggestions for coffee shops, restaurants, sites not on the beaten path, would love to hear about those, too.
If you've not been to Ostia Antica, check it out and see if it interest you. Easy to get there on public transit, very similar to Pompii, and with an early start you can be back in the city by mid-afternoon.
I plan on being in Rome in June. Being my first time in Rome, I’m playing it safe by staying at brand name hotels. The Double Tree by Hilton Rome Monti looks nice. It is a 7 min walk to Roma Termini. I couldn’t book a room there because it is hard to get a room that can accommodate 4 people. I booked at the Best Western Hotel Artdeco instead which is about a 11 min walk from the train station. There is a Beat Western Royal Santina that is 4 min from the station but is all booked up. Hope this helps.
You might look at staying in Prati, which is the area by the Vatican. It is well-connected to the Centro Storico and Trastevere, and away from the Vatican is very residential, not touristy. Great Sicilian food at Siciliainbocca where the only Americans we ever saw were our guests.
I don’t have a specific hotel to recommend but try Booking.com or pull up Google maps for the area and look at the dozens of hotels displayed there. I do that all the time to locate properties in the location I want, then I seek out details and reviews. Try La Pratolina for unique pizza, reservations essential.
Testaccio is a cool area many don’t get to, especially the museum Centrale Montemartini in an old power plant and the new+ish Testaccio market.
Also the Gianicolo (Janiculum Hill) is fun to explore.
There a book called “Rome the Second Time” that offers itineraries for repeat visitors.
We have stayed in the Prati area our last 2 visits to Rome and would again. Our recent stay was at Hotel Isa. It’s close to several bus stops, easy walk to several areas and lots of great food. It is a more regular neighbourhood of locals and we love it.
Perhaps look at "The Beehive" which is only 2 blocks from Termini station. I am staying there night before I leave in November...mix of hostel and hotel. I booked a private room with en suite and was quite reasonable. Also in my 70's (solo traveler) and am excited to stay there...perhaps will suit your needs too. My priority was close vicinity of train station to return to FCO next day. Enjoy your trip!