Spent a week there last summer and did all the usual. Just wandering round and popping into *any* baroque church/basilica was mind blowing. They will blow you away. One moved me to tears.
Cat Sanctuary at night. We were wandering back to our our hotel and stumbled across it.
The Trajan Market museum is really good and well done.
For me the museum in the Villa Borghese park was just astonishing. Buy tickets only in advance.
As a typographer the Trajan Column was a bit of a pilgrimage and a highlight, too. Bit geeky, mind.
Make sure you eat in Trastevere. Find the pokiest backstreet restaurant away from the tourists and enjoy the best Italian meal you’ve ever had 🙂