The US certainly would not resort to nukes over those islands.I'm having difficulty seeing us trading nukes with China over the Diaoyu islands. Yes, there's the alliance and all that, but Shanghai for Los Angeles and Beijing for Washington D.C. in the name of Japan is a bridge too far.
But they would over Tokyo being nuked by China. That was the scenario that was being followed here...if China resorted to nukes against Japan. I do not believe China would nuke Japan over those islands...but if she did, then the US certainly would most probably respond.
If the US allowed a close ally like Japan to be nuked and do nothing, then all credibility and all defense treaties (including with NATO) would be immediately rendered worthless. Not going to happen.
As I said, if it was a convetnional, limited engagement simply over the islands, the US would probably give material support to Japan in terms of intelleigence, recon, surveillance, etc. and not much more. Like the US did for the UK during the Falklands. But all of that would change in an instant if China started losing such a scrimage and then resorted to nuclear arms against the Japanese home islands.
Let's all pray to God such madness never occurs.