There is no most important index in Asia ( and Europe and US). there are various major indices in Asia ( and Europe and US). quite a few posters have already answered the question.
The Nikkei225 is the most significant because it has the 2nd largest index futures market behind it. The volume is mainly the big boys such as Goldman and Saxo, not to mention the occasional few 1000 lots from CIS.
Think you might need to define your question better. The way I read it, most watched, being most traded by others in the world besides in the local market which some have mentioned the Nikkei 225. But then also most watched could be Shanghai SSE Composite Index representing the second largest economy in the world. Which is it?
Don't search for the magical best. Take a look at them all and decide which would suit your style and timetable. To me, Nikkei is as slow as a wet week. I prefer HSI but HHI, Kospi, Nikkei, STW, Nifty or something else might suit you better. Most have minis for your initial experiments. Most watched doesn't matter imo, most tradable for your methods and personality does.
I know a few good traders that are trading stuff they don't like to trade. Yet, they trade them because their trade methods work best in those particular markets. Simply, the goal is to make money and not trade what's popular, heavily marketed by the broker or forum fan favorite. wrbtrader
Different traders would come up with different answers on the basis of what works for them. I have recently invested in Shanghai Composite (China).