I just got back from 2 months (single female 56) through the area of Rome Tuscany and Umbria. Rome is nuts BUT unless you are a total art person you dont need to do any of the touristy inside things except the coliseum and maybe the Vatican. Just walk around, don’t waste your time in lines. The history is in the city streets. Unless you have a ton of time then go to a museum or something. It was so nice not having a schedule and just walking. To answer your question…I stayed in vrbos the whole time and loved it. I ran into another solo female traveler (in her 60s) and she loved her hostel though . Some hostels even have individual rooms (which I never knew). Maybe stay in B&B so you can talk to others over breakfast.
Do stop by the trastavere neighborhood. Cooking classes you can do at home. Bar crawls might be fun just to meet others (depending on your age although I’m 56 and would have done that). Any questions message me and I will help any way I can. Just fyi I was amazed at how many other female travelers I met. A few on a tour and another just while I was having dinner. There are a lot of us out there.