I think for me it would be Vanavaasi Rama, before Sita's abduction. That's when Rama actually lived his life, not dictated by anybody, not having to fulfil anyone's expectations, not requiring to act according to the society's views.
First few years of his life till his Vanavasa, he was Dasaratha and Kausalya's son, Vasishta's student, Vishwamitra's student and on the whole the prince of Ayodhya. Lots of decorum was required.
After Sita was kidnapped by Ravana, he had to behave as per the devas' wishes i.e. go fight Ravana, kill him, that's why you have taken avatara.
After his Pattabhishekam, he had to follow the citizens' wishes. Yatha raja Tatha Praja.
So, yeah, the Rama of the first twelve years of exile was the one with the breathing space.
IMO, that was when Rama was actually free to behave as himself. And that's how I like him.