This is a really interesting topic to me, and something that I am planning of writing my paper on. Many environmental scientists have actually backed nuclear power recently, believing it to be necessary to replace coal and oil while we transition to more renewable energy sources. When I try to form my own opinion on whether or not I believe nuclear to be a good option for our future, it is usually the issue of waste that gives me the most trouble.
On the topic of sustainability, I usually look at nuclear power compared to coal or natural gas or some other form of electricity generation. When looked at like this, nuclear clearly seems the better option, being much cleaner than coal, and even safer, as stated in this article by NASA. However the waste produced by nuclear reactors, while not immediately damaging to the environment, has the potential to harm greatly if is not contained properly. Also, because these wastes will remain harmful for so very long the issue of long term storage comes into play as we currently do not have an easy way of disposing of them.
Because the responsibility of storing these wastes will span multiple generations, this makes cost-benefit analysis difficult, as a large part of the cost will not have to be paid by the generation that reaps the benefits of nuclear power. However, my current opinion is that the benefits of nuclear power do outweigh the costs, even factoring in the long term waste storage. The harm caused to the environment by its alternatives, specifically coal fired power plants is immense, and if we could sooner get these plants offline it would be very beneficial. Disposing of the waste should be done in the most environmentally safe way as possible, though this might cost more than other methods of disposal, in the long term it makes the most sense. The fact technology could develop a way to make these wastes less harmful in the future is a hope, but it is not guaranteed.