Ancient Rome was famously composed of seven hills, but there are even more hills in modern Rome that weren't even included back then. One of them is the Janiculum Hill, or Gianicolo in Italian.
Gianicolo Hill sits on the western side of the Tiber River, near the Trastevere neighborhood, and takes its name from the god Janus – there was once an ancient cult to him located on the hill. Today, attractions on the hill include the San Pietro in Montorio church, a Bramante-designed shrine on the supposed location of St. Peter's crucifixion, and a botanical garden associated with the University of Rome. But the main draw is the view overlooking Rome – it's one of the best in the city.
The Gianicolo Hill is a public place, so it's open at all hours and it costs nothing to explore. There are several buses that will get you up to the central Piazza Giuseppe Garibaldi if you don't feel like walking, too.