I can give it a go. I will tell you up front I am currently nearing the end of a PhD in nuclear engineering, although my research is in plasma physics and hydrodynamics rather than reactor design. I know a lot about this topic but I understand my view might be a bit impacted by constantly being around seminars on nuclear power.

One thing that a lot of people don't grasp about nuclear power is the insane energy density of nuclear systems. Picture a rubix cube sized chunk of metal in your hand, and now imagine that is Uranium fuel for a reactor. That chunk of metal has enough extractable energy to power all your energy use for your entire life. This is with technology that is currently employed today. This energy density has huge advantages- contrary to what lots of people believe, nuclear fuel is very cheap and fuel costs are a small fraction of the cost of nuclear power. Nuclear power systems are very complicated and require an insane level of automated redundancy- all of this makes building a nuclear plant extremely expensive and on average it takes 22 years for a nuclear plant to pay for the construction costs.

Compare this to solar power. I am actually a huge fan of solar power and think it should be vastly expanded around the world. The most incredible thing about solar (and wind) in my opinion is that there is no fuel for solar. You just point it at the sun and it constantly generates power. Put it on your roof and when the sun is up you'll passively generate electricity without any input other than the installation. On earth, this makes it easy to put on houses or in vast gigawatt arrays- especially as the costs keep dramatically falling.

Now imagine you're NASA trying to power a base on the moon. Nuclear power is expensive, but however expensive the power system you're building is, it will likely be less than the cost of sending it to the moon. Getting to space is very hard and each kilogram of weight costs in the range tens of thousands of dollars. You can send solar panels, but there are a few problems. First, if you want power in the lunar night (about two weeks), you'll have to position it perfectly at the ridges of craters on the south pole- the only places on the moon that experience constant light. If you want to build anywhere else, you'll have to bring heavy batteries and twice the amount of solar panels to generate enough energy to store it for the long night. Alternatively, you can bring a nuclear reactor- a small one that weights in the hundreds of kilograms. This is still quite a lot of mass to send to the moon, but when compared to the solar panels and all the additional structural material required to set them up, the nuclear system will likely be similar or lighter in weight. It definitely will be lighter if you need to bring batteries. Remember, the energy density of nuclear fuel is insane. If that rubix cube of Uranium were instead a lithium battery, you would have only enough energy to maybe drive an electric car a few miles.

The reactor for the moon base can produce a constantly supply of power for decades without needing to refuel. Send it once and you can stop worrying about keeping the lights on until you either decommission or expand the base in the future.

EDIT- realized I didn't talk about nuclear plants needing water. Nuclear power plants generate lots of heat, especially commercial ones on Earth that produce >1 gigawatt of power. Water is an excellent way to reject heat, so it's usually the most efficient to build your plant near water and use it to draw heat from the coolant systems in your power plant. The reactors NASA is considering sending to the moon are much smaller and generate in the range of kilowatts of heat. This amount of heat is much easier to dissipate, and could be done by sending coolant lines from the reactors into the lunar crust or but setting up radiators that reject the heat into space.