Nuclear energy is a renewable energy source that can be widely available if more people supported it. So we can look it at that way, and see that it can help lower costs simply because it is renewable. However, we can also look it its positive effects on the environment. If we can reduce our uses of natural resources and fossil fuels, that will lower future costs of environmental damage. So it is cost-effective in more ways than one.
Over the long-term, nuclear power is cost effective because nuclear energy doesn't cause greenhouse gas carbon emissions. The only atmospheric particles released by nuclear fission reactors are water droplets from steam. Nuclear energy costs more initially, but in the long term prices will come down the more reactors are built. Supply and demand dictates that when more nuclear reactors come online and replace coal-fired plants, the energy will become cheaper. When coal supplies start to run out, that form of energy production will become more expensive. It's only a matter of time before nuclear power is the preferred method of steam production for turning turbines.