We already have safe, reliable nuclear power plants. We have them all over the world. The challenge with nuclear is no different from any other project that deals with hazardous processes (and this includes coal and oil power plants among many other things): reasonable standards for building, operation, and inspection free from bribery, corruption, and incompetence, which are rigorously enforced. In some places (mostly the western nations), this isn't that hard to do. The designs are already rock solid and have been for a long time (minus the RBMK reactor designs, which were never a safe solution, but which weren't designed with safety as a high priority - they were experimental reactors and weaponized fuel factories). The plant at Fukushima was an early design which would have still be safe had the company operating the plant bothered to perform the remediation steps provided by the design manufacturer (GE) for known problems in the design. Had the regulators and inspectors forced them to perform those steps, even the plant's owners' negligence wouldn't have been allowed to carry the risk of the catastrophic failure following the earthquake and tsunami there.
We have great designs which have run at >90% capacity for decades on end without issue. We know exactly how to operate nuclear safely. In fact, per kwh, nuclear is the safest power production in the world. (yes, safer than hydro, solar, and wind - look it up, you'll find workers dying from falls, burning to death, drowning, etc). What we need to do is come up with a way to supply power to places with shitty governments at a rate that's cheaper than fossil fuel plants (for the environmental impact issues there) without giving them the opportunity to fuck up nuke plants or weaponize them. Solar, wind, hydro, and geothermal will all play their parts in our worldwide energy future, but the fact is that well-run nuclear is our best, safest, most sustainable option for a backbone. Nothing else scales like it except fossil fuels and those wreck our environment pretty badly until they're all used up (which is pretty shortly - relatively speaking).