Once we have gotten rid of coal power it is a good idea to replace nuclear with e.g. solar, but not before. As long as we have coal we need to replace it with something safer and sustainable, currently nuclear is often the only/best option.
Solar panels (like wind) are great but they only generate electricity when the weather and time of day/year permits. We need electricity 24 hours a day to keep society going. I'm at about the same latitude as Scotland, or southern Alaska. Today the sun rises at 8:30 and sets at 15:30, the suns altitude at noon is about 10 degrees over the horizon. So we only have about 7 hours of sunlight and when we do it's pretty dim. I.e. we couldn't hope to rely only on solar during the winter. There are all kinds of proposals of how you might work around that, but at the moment it's a bunch of more or less fanciful theories and ideas. One of them might turn out to be practical, but no complete solution exists today.
Science/engineering isn't magic, we can't just pull the technology we want out of a hat when we need it, so you can't just assume that if we throw more money at research and development we will get a solution in a timely fashion. Fusion power is a good example of that. We have been investing enormous amounts om money on fusion for a long time, hoping it will solve all our energy problems. Despite that, while fusion researchers are making some progress, they still have no idea when, if ever, they will have a working fusion reactor.
We could try and be more energy efficient, and we should, but that requires large sacrifices that not everyone appears to be willing to make right now. And there is a limit to how much energy we can save: we need some power, it's not just a convenience, it's what makes all the machines, factories and hospitals work. They produce our food, delivers drinking water, medicine and healthcare. It's essential to society.
Besides, making all these changes (energy saving, solar power, etc) will take a long time, even if everyone would agree to do it (which they currently do not). We should have begun 30 years ago. Look around you: nothing is happening we are using more and more energy, the amount of coal burnt isn't just increasing, it's accelerating!
So while we are waiting for people to begin saving power and inventing solar power storage solutions we should use whatever methods are available right now to replace coal. The most obvious choice is nuclear. It exists and we know it works and as a bonus it's actually pretty safe (contrary to popular belief), as I've pointed out it's even safer than water power if you look at the statistics.
While it's true what someone said: it takes a long time to build a new nuclear power plant, and we couldn't possibly replace all coal plants with nuclear quickly enough. What is happening right now is that people are irrationally shutting down nuclear reactors and replacing them with more coal and gas (that's what Germany did recently for example). When building new power plants people choose coal instead of nuclear (like South Africa decided to do recently). That is really bad for all of us; it's bad for our health, it's bad for the environment, it's bad for the climate (which in turn, in the long run, might even be catastrophic for us).
In order to get rid of coal as fast as possible we should expand nuclear power as fast as possible (while still maintaining a high safety standard of course), just as we should be expanding solar and other renewable options as quickly as we can. Then once we have replaced all the coal power plants we can begin replacing nuclear.