If you only count the reactors that are already built and still operating, they are pretty cheap sources of electricity. The old nuclear projects that were abandoned before completion won't be part of your "power per dollar" denominator. The reactors that were shut down 10 years ago because they were too expensive to keep running will also be missing from the denominator. The late and over-budget reactors that have yet to enter service will be missing from the cost denominator as well. Once you limit the field of inquiry to the surviving, operating nuclear plants, they're pretty affordable.
If you interpret the question as meaning "nuclear energy is currently the second cheapest per watt [to add to a nation's electricity supply]" -- no, that's incorrect for anywhere with half-decent wind or solar resources.
The final question that prevents me from being a 100% renewables triumphalist: what happens to the relative cost of nuclear vs. more renewables + storage as renewable penetration rises? Storage is hardly needed at present penetration levels. Only a modest amount of storage (overnight) may be needed for 50% or even more penetration. But what happens at 80%, 90%, 100% decarbonization of the electricity supply? It's possible that even expensive new reactors will be cheaper than reaching 100% with storage and renewables alone. It remains an open question.