Nuclear power is green — it has almost no impact on greenhouse gasses (considering the total lifecycle CO₂ emissions). It has less impact on greenhouse gasses than solar or wind.
It's true that nuclear waste has to be handled properly, but the engineering challenges have been more-or-less solved.  Nuclear waste disposal remains a problem only in the political sphere.
While we should move to solar and wind power as quickly as possible, they won't be a complete replacement for nuclear in the near future. There is noticeable gap between electricity demand and renewable energy supply — renewable energy production tends to peak in the middle of the day, while there's quite a bit of demand in the mornings and evenings.
Energy storage will eventually solve this problem, but current energy storage solutions are too expensive to be used on a widespread basis.