Hi the,
As a single, female traveler, maybe you'd like the Trastevere area. It's quaint with resemblance to "a little village."
Check out this video from The Roman Guy
https://www.youtube.com/watch?v=v75H2alRIW4
Sean F. is one of the leads and a cutie. I don't know him personally; just like to watch their vids. And Sean sprinkles his sense of humor into some videos.
I traveled solo around Rome (twice in the last two years) and had no issues with safety or harassment. Many are helpful. There are police and military in and around major attractions and major neighborhoods.
Termini gets a bad rap, but I had no issues or fear. I stayed in a very nice hotel and often ate at a favorite restaurant a couple of blocks away. My bedroom window on the fourth floor looked out to (into the distance) The Diocletian Baths. Lovely.
Rome is relatively safe. Keep a big city awareness. Keep your wits. Keep a positive stance while walking about. Watch your bag. Don't put all valuables in your bag. I don't know if you plan on using a cross body (I suggest) or a backpack. Don't hang it (absentmindedly on the back of chair anywhere. Don't put it on a table where it's up for a grab.)
Anyone approaching you to buy something, just say "No Grazie" and keep on walking. Unless you want a Pashmina for 5€ lol.
If you'll be around the Pantheon (Piazza della Rotonda) or the Colosseo and want an exclusive picture with a gladiator, keep in mind, they will expect much euro to have their "mugshot" taken by you or with you.
Maybe do a search in the above box - put key words in such as "Trastevere hotels" and see what threads pop up. Some may be years old and info no longer accurate. You can narrow down/filter the replies by date.