Cesium 137 with its half-life of 30 years will hang around for 600 years. Do not be surprised if you learn that the nuclear industry makes billions of dollars by being a part of government's policy of burial of nuclear wastes. It is not in their financial interest to try any other process. They are not idealists. Although above-ground storage has the advantage of access to being monitored, it is still not without unsolved dangers.
Nuclear waste is highly unstable and reactive.
These tanks contain plutonium wastes and organic materials. Chemicals in the tanks break down, producing hydrogen gas, increasing pressure inside the tanks. This lays the conditions for an explosion, which would spread contaminants into the atmosphere, the land and the water, not to mention the people and the animals. In 1957, similar waste storage tanks exploded at the Russian Mayak plutonium plant and contaminated hundreds of square miles in the southern Ural mountains. This disaster caused thousands of casualties.