The Ryukyu islands considered independence after WWII but thought staying with Japan would get the US occupation out of Okinawa earlier. As it turned out Japanese politicians favoured having US forces in Okinawa rather than Japan proper.
What if Ryukyu declared independence in the late 1940s? What would its role in Asia be during the Cold War and the present day? What would its international relations be like?
They'd probably be a poor backwater government dependent upon Japanese or Chinese help and imports. IIRC Okinawa is currently Japan's poorest prefecture--things might change dramatically in this TL, but I can't see the Ryukyu Islands developing, by themselves, a thriving economy in sixty some odd years. There is also the fact that the US military would, by that time, have set up large military bases in the island chain. I can't see them being that willing to pack up and leave, which may mean some definite friction in East Asia.
In terms of the Cold War, though, things could get a lot more interesting. If we say that the Ryukyu Islands do declare themselves independent, but struggle to maintain a decent economy, what would the effects of that be on the political climate of Asia in the 1950s and 1960s? WI the islands moved closer to China politically and economically than Japan? And if the US kept a strong military presence on the islands, what would the chances be of a guerrilla war developing between the Ryukyans (sp?) and the US?