More solar cells, batteries and/or capacitors can solve the 14-day lunar nights. I'm not saying I reject nuclear power, which has it's uses. I just want to keep this discussion fair.
Most fissionable materials with useful half-lives will be around far into the future, and mankind's current disunity doesn't give me much confidence in future proliferation of fissionable materials into unsecured environments. On the other hand, sending fissionable materials to the moon would undercut diplomatic efforts to prevent today's earth-bound nuclear proliferation.
Really, the nuclear option should only be used where no other option is feasible or practical for the mission at hand, and where a reactor damaged by a faulty landing would not present a problem for the destination environment, the mission or for future missions, and where we can be sure it will remain secure even far into the future.
As it turns out, the most reasonable locations for lunar facilities are at the polar regions, where natural terrain may afford the best chances of survival by shielding from the solar radiation, allowing solar energy collection on ridges and possible access to water ice in the craters.
Anywhere else on the moon would require the landers and base facilities to be radiation shielded. Perhaps this could be achieved using solar powered electro-magnetic shielding, or by digging into the regolith or covering prefab facilities with it, but water supply will be the biggest issue.
Research on lunar resources is still incomplete. We've only really scratched the surface, so I wouldn't be so hasty to dismiss the moon as a source of useful materials. We're already aware of at least aluminum, silicon and oxygen components in the topsoil, and the regolith is useful for insulating against solar radiation. With these resources, you've already got some of the basic makings of solar cells, aluminum structures, glass, silicone sealants, etc., so building a presence there is much easier with solar. This is the most promising course so far to achieve lunar facility autonomous operation.
Access to fissionable material on the moon is a problem. We'd probably be digging for years before making a find. Perhaps landing a nuclear plant on the moon would only be necessary in order to process enough lunar resources to enable the settlement to produce enough of it's own initial solar power collection facilities to enable growth of the settlement.
Lumping hard radiation from fission with background and solar radiation to justify putting it in close proximity to humans on the moon is just plain stupidity. Never underestimate the risks and complications of having a nuclear power plant in close proximity to humans. Be realistic.
Every power option available, even solar, brings risks along with the benefits. If you're going to bring nuclear reactors to the moon, use them for backup and for powering missions to destinations further from the sun, where solar loses it's effectiveness.
If you must use nuclear power, make sure the reactors are as safe and shielded as possible, to protect the crew and to preserve the environment at the destination.
The moon may lack an atmosphere or magnetosphere, but that doesn't make nuclear plants any safer there than they are on earth. Considering the forces involved, the risks of launching and landing a nuclear plant of any size are too big to ignore. Just because folks aren't yet living there doesn't make it right to do things carelessly.
Some destination environments are protected by atmospheres and/or magnetospheres, so inserting a nuclear plant into those environments could result in contamination of an otherwise low-radiation environment, especially if the lander crashes. Therefore, to comply with environmental concerns, either ban this practice or at least ensure that the lander uses soft-landing techniques with enough redundancy to ensure safe landing.