Palatine hill is right next to Colosseum on the hills, and you can actually purchase a combo ticket including entrance to Colosseum, Palatine hill and Forum Romanum which I highly recommend. Palatine hill is the centremost of the Seven Hill of Rome and hast hosted imperial Palaces since the time of Augustus.
In addition to its own gardens and ruins of palaces which provide a nice surroundings for spending even few hours on a pretty day, Palatine Hill also offers a stunning view over Forum Romanum. Forum Romanum is where the city center of the ancient Rome used to be. It hosts several temples, places of justice and important buildings. When you explore the buildings you can start to imagine what life used to be in Rome before its collapse.