The Colosseum (Colosseo) located in the historical center of Rome. It is well connected with public transportation and right near the ancient construction is metro stop called “Colosseo” with the bus stop and  tram stop nearby.

Such important points of interest as Piazza Venezia, Circus Maximus and Roman Forum are near the Colosseum

If you want to reach the Flavian amphitheater from the airport, the best way will be to take fast train Leonardo Express from Fiumicino airport or bus from Ciampino airport which goes in both cases to Termini station, while from Termini you can choose between one of many buses that go to Piazza Venezia (46, H, 64, 170) and reach the Colosseum by foot within 5-7 minutes or use metro from Termini to Colosseo stop.