From the Perugia Train Station, we took the train to Rome's Termini Station (10,50 Euro Regional = 3 hours, varies). There's a lot to do in this historic city. Rome has the Coliseum, the Roman Forum, Trevi Fountain, Monument to Vittorio Emanuele II, Piazza Navona, Spanish Steps, St Peters Basilica, Vatican City, Pantheon, Castel Sant'Angelo, the Tiber River and dozens of other attractions. From the Roma Termini Station, you can take the train straight to the Fiumicino / Leonardo Da Vinci Airport for 11 Euros. It takes 31 minutes to get there, coming at every 31 minutes at 0:22 and 0:53 (example: 1:22pm, 1:53pm).
The Admission Price to go inside the Coliseum is 12,00 Euro (not a guided tour), guided tour costs an extra few Euros. The Roman Forum (The Ruins are the oldest structures of Rome)
The Trevi Fountain: A traditional legend holds that if visitors throw a coin into the fountain, they are ensured a return to Rome. Have your back towards the fountain and throw the coin with your right hand over your left shoulder.
The Vatican - St Peters Basilica: Entry to the Basilica and the Tombstones are FREE. There is a line (we waited for 5 minutes) and we went through security (metal detectors). Unfortunately, we didn't get to go to the Vatican Museums (those have entrance fees)...Sistine Chapel is nearby.
Castel Sant'Angelo (has entrance fee) The Pantheon - a temple built to all gods of Ancient Rome (free entry)