Hello gab,
I've not taken a tour, but a quick read on the seven-day Rome tour lists some free time. Just read through each day's activity list. I think some people add on a few days before or after the tour if it's doable for them financially and time wise. Of course, traveling independently has its own freedoms and rewards.
Rome is definitely an outdoor walking museum in itself. What are your interests? More churches? More museums? A simple walk around the city? Depending on the time of year you are going, check out some Rome activities related to that time of year. You may be able to be part of a celebration going on or may be able to secure tickets (free or for a small sum) to attend an event going on.
I went to Rome, two consecutive years so far, in the month of December. I like to mingle a free-spirit attitude with some planning.
You never know who you'll meet or what you may come upon.
On my first visit to Rome, I came out of the Pantheon (around lunchtime) and was greeted with street musicians setting up near the Obelisk. I listened, mesmerized with the lead singer's voice. His band mates were terrific with each of their instruments. I was hooked. Literally, "a concert." I sat on the wall outside the Pantheon and listened to them for about an hour & a half; maybe two; until they stopped. I caught them at Piazza Navona and Campo de' Fiori on other days for a bit.
Another day, I was walking around lunch time, and I heard this "marching band" in the short distance. I couldn't see them yet, but I followed the music. There were musicians, all dressed in Santa suits blaring their horns and banging their drums to jazzy renditions of Christmas music. It was a blast. People were dancing, clapping and singing.
On both trips, I met people; had great conversations in piazzas and or my fav restaurant. (I made a few friends my first trip; met a few family members.) My visit the second year involved hanging out with them on different days for breakfast or dinner, a drink or cafe or spending some time chatting at the stores they owned or worked in. It was tons of fun. They were generous and very kind.
This past year, I was talking to a woman who worked at a gift shop at St. Peter's; she gave me a free, limited invite to attend a special mass given by Pope Francis in honor of Our Lady of Guadalupe. Stunning Mass!
If it coincides with your visit and your interests to get a taste of an opera, make your way to St. Paul's (Within The Walls.) They hold special concerts at the church. Check their website for availability and presence of musicians and operas.
Until you're there, in front of some of the most beautiful buildings ever, no picture or description can do a true justice. Getting "lost" and discovering something out of the ordinary? It's endless; especially in a big, bustling city such as Rome. You can walk the city forever and still come upon something new.
With the RS guided tour, you'll be taken around to the most highly attracted sites. You'll also learn to navigate the city's transport system and streets. I stay in the Termini area and never encountered any danger or issues. But, people need to exercise common sense too. I didn't wander around Termini in the wee hours. I wouldn't do that in Boston either, and I am very familiar with the streets and neighborhoods.
Riding the buses, especially #64 (or #40 Express) was fine. Just keep aware of your valuables. I would advise that to people riding on Massachusetts buses and trains too.
I rode the Rome Metro once, during the afternoon (about a half hour ride) back to Termini. No issues.
Get a head start and watch some YT videos to get a flavor. Rick Steves and The Roman Guy. I really like to watch The Roman Guy for a number of reasons.
Have fun on your trip!