Recommendations for unusual sights requested please!

My partner and I are travelling to Rome for the Italy/Ireland Six Nations game next year. We plan to spend some time in Rome and travel to Florence before heading back to Rome (a total of 2 weeks).
We will be visiting all the popular tourist attractions as we love art and history but I’m interested in anything that you think is a must see that is often missed. My partner is very interested in photography so any recommendations related to this is a bonus!
As we will have a lot of time to explore any day trips/nearby cities you recommend is also very useful.
Thank you in advance!