Florence in the late Gothic from Smarthistory
The schedule for your time in Rome looks very full, and there are plenty of things to do—like eating and shopping—that you might use for your free time. I have one suggestion: you should visit the Vatican Basilica of Santa Maria Maggiore.
Why take the time for this? First, it is an extremely important—and beautiful—early Christian church, built in the fifth century. Although the exterior has been changed over the centuries, the interior retains its famous early Christian mosaics and generally recalls the appearance of early Christian basilicas.
Second, it sits in a lovely piazza that includes (FOUNTAIN—OBELISK)
And third, it is just a few blocks from your hotel. It opens early in the day, perhaps before your other activities start, and you might be able to walk over to see it.
Here is a wonderful short video from Smarthistory about the basilica. At this page, you will also find other links to information about Santa Maria Maggiore