The problem of nuclear waste is twofold.
There's the technical problem with nuclear waste, in that some of these substances are going to be hazardous for hundreds of thousands of years. That's an inherent property of these materials. There's no amount of research that's going to change that property.
The second thing is that the way to try to deal with this problem has typically been to try to do what's called “reprocessing”. Sometimes, euphemistically, it's called “recycling”. The problem there is that you cannot get rid of the radioactivity, so what you're doing in reprocessing is moving the waste from one location in a solid form into multiple streams of radioactive waste. All of them have to then be dealt with, so it's actually making the problem more complicated.
I don't see any promising research as such. The only thing that most countries have decided to do is to say they're going to build deep geological repositories and bury the waste there. Most of the research there has to do with trying to understand how you can persuade a community to live with this hazardous product in their vicinity for millennia.
That's not an easy problem. Again, it's like many of the other things you said. Communities are very different, and each community has its own set of concerns that will have to be addressed.
Most of the research in nuclear waste that I see as promising goes in that direction—the social direction—rather than the technical direction.