I have visited storage- and test facilities that are within salt and clay (Opalinuston) lithologies. What are other lithologies that are considered for the storage of nuclear waste and what are their advantages?
Nuclear wastes should be stored in containers designed to contain and isolate radioactive material from the environment. One possibility for the storage of these containers would then be to place them in a repository located in a tectonically stable, dry, geological formation.
As far as lithological characteristics are concerned, it would be best to locate the container repository in rock having mechanical and chemical properties that would limit transport properties and slow or contain the spread of material in the event of a container failure.
Advantageous properties include:
1) low permeability and few joints and fractures
2) low strength, so that plastic deformation of the rock would tend to reduced stress and close fractures.
3) mineralogy-fluid chemistry that tends to bind and immobilize radionuclides.
Volcanic tuffs (zeolite-rich), salt deposits, and clay deposits would be examples of lithology having some (but not necessarily all) these characteristics. Granites and columnar jointed basalts may be examples of less advantageous lithology.
As @david valentine said, the lithology would be only one of many factors that need to be considered.