I think that many people don't notice this part of the Roman Forum or maybe they just don't want to pay extra. To go into the Palatine Hill you have to pay 12.000 L, but it is well worth it.
The day I went to the Forum it was incredibly crowded as I'm sure it is every single day(and for a good reason). So going up to the Palatino was a nice change of pace.
You feel like you're entering someone's terrace and garden...From the terrace of a house you can see the entire Forum. It's quite a breathtaking view! And what made it even more special is that I had the whole terrace to myself(later some people did come, and so I moved on). You start imagining people walking through the streets and gardens. You can almost see the people and hear them laughing(and before you say anything: I'm not crazy!).
But there is so much more to the Palatino. You hear the water falling; you go up and down stairs, through gardens, palaces and houses(well, the ruins, but just the same)...It's like a maze and you feel like you're the first person to discover it, because there is simply no one around you...It's quite scary sometimes, because you can find yourself in some really dark rooms.
To get there:
Take Metro A to Colesseo. You could either enter from inside the Forum(Via Sacra) or from Via di San Gregorio, which is just outside the Forum .