Efficiency
Nuclear plants can produce a large amount of electricity, up to about 2GW, which is comparable to coal plants. More importantly, however, is the amount of fuel required to generate this energy.
At the atomic level, the thermal energy released in a fission event is 200MeV, compared with only a few electron-volts produced each time a hydrocarbon molecule is broken down by burning carbon-based fuels. As a result, a single nuclear-reactor fuel pellet just 1cm long can produce the same amount of electricity of 1.5 tonnes of coal.
Source: P. Norman, A. Worrall, K. Hesketh, Physics World, Vol 20, No 7, July 2007, page 25
Reliability
There is no need to worry about interruptions to the power supply: as long as there is uranium, there will be power. This is a stark contrast to most renewable energies which depend on the activity of the weather.
As a result of this, nuclear power would be suitable for providing a base load which would be present at all times. Pumped storage and renewables could then provide temporary energy to cope with spikes in demand.
No greenhouse gases
There are some greenhouse gas emissions associated with the life cycle of uranium, as gases are emitted as it is mined and transported and so forth, however this is significantly less than the emissions associated with the burning of fossil fuels.
Essentially, nuclear power would be "carbon-zero" if the the uranium were mined and transported in a more efficient way. There are of course issues with radioactive waste, however.
Supply
It cannot last forever, but at least the fuel is more easily accessible than oil. 24% of uranium resources are in Australia, and 9% in Canada (source). These are hardly politically unstable regions.
Safety
We frequently hear reports of explosions at gas plants, accidents at oil refineries, even dams breaking. The fact is that nuclear power has in fact caused fewer deaths than fossil fuels.
It could be argued that this is because its implementation is not as widespread, but the fact remains: as long as the reactor is well designed and waste is properly dealt with, the risks of death are minimal. Take a look at this graph for more details:
Granted, the explosion of a gas facility would not be dangerous over such a vast area as the accident at Chernobyl was, however modern reactor design eliminates this risk.