I really enjoy theoretical questions like this because I've always been really interested in history. If this wasn't an Asian drama forum my answer would be the Roman period - right after Caesar dies and Augustus takes power. But it's not a clear, clear #1 answer and I would be super excited to go anywhere.
I think it would be crazy to experience the Warring States period of China or some of the early Korean peninsula kingdoms (Baekje, Goguryeo and Silla). Admittedly I don't know much about Japanese history beyond the few time travel shows involving Nobunaga but it would still be interesting to witness that period.
So I guess 1. Warring States period of China 2. Early Korean history when there were 3-4 kingdoms sharing control over the peninsula.
It allows for a diversity in culture, style and progress even if things are more dangerous because there is always a chance of war.