What is important to highlight is that nuclear wastes are rather small compared to those wastes which are produced by fossil fuel electricity generation. Apart from that, there are proven ways in which it is possible to get rid of nuclear wastes in a safe way. What should also be mentioned is that there are different types of radioactive waste. Thus, some of those types are of low level while others are of very high level.
Here are a few ideas on how to dispose of radioactive fuel. The most common type is direct disposal which presupposes that the fuel will be stored at a geological repository. Then there is aqueous reprocessing during which uranium and plutonium will be removed. Probably, the best way is the advanced electrometallurgical reprocessing the idea of which is to get rid of plutonium, uranium and minor actinides so that to recycle them later on. In such a way, it will take 300 years for the wastes to reach the same level of radioactivity as the original one.