Today's nuclear (e.g. AP1000) is splendid technology by any measure. AP1000 builds are designed to last 60 years but should be economically maintainable for hundreds (life of the containment, which is the expensive part).

Amortized over 40 years, the nominal cost of nuclear is very low - on par with coal. The barrier to rapid buildout is the high upfront cost. Operation is almost free. Standardized plant designs like the AP1000 should cure most construction delays. The Chinese builds currently underway were ahead of schedule last I checked.

The externalities of energy sources are poorly studied, nuclear being by far the best-studied. In the US, waste disposal is fully paid per kWh and has been since the early '80s. Mining and everything to do with the fuel chain is far cleaner than anything else, including wind and solar (it was my job to study these things for a certain fruity company that has no vested interest in any particular technology). Regulation in the US is also paid-for by the industry (NRC charges astronomical fees).

As you probably know, safety per GWh is found to be on par with wind and solar by every study out there.

The factor of 500 corresponds to burning Th232 instead of U235 (490 precisely). Burning U238 will give you a factor of 140 instead. Either will additionally save the need for enrichment, though turns out to be a tiny factor. High-temp operation with either fuel will get you 5/3 in the thermal efficiency dept. Atmospheric pressure operation gives you something like a factor of 10 on plant materials, which is not terribly significant on a per-GWh basis.

All of these have been demonstrated - most decades ago. There's no basic physics, just engineering. 10 years to market for any serious effort. Where you might need 50 years is something like a dusty plasma reactor. Those directly convert fission energy to electricity (thus reaching efficiencies over 90%) and can also enable interstellar travel. Still easier than fusion.

For solar efficiency there's a factor of 3 to the Carnot limit and wind is less than a factor of 2 from the Betz limit. Further improvements can come by making the collectors lighter. But solar cells are already thinner than can weather the elements and so are mounted on substrates, under cover glass, on stands and tracking motors etc. About the best that can be done is mirrors with a central thermal tower, and this is being done today. Tethered wind has potential for reducing the utterly absurd material requirements of current turbines - Makani says a factor of 5.

Those are available improvements, since you mentioned it. Absolutes are what count. For solar, plan to cover about the same amount of land as has been paved to date (assuming ideal location).

I don't know what renewables are. Do they include geothermal? Howabout induced geothermal? What about fission (supernovae aren't renewable)? Biofuels (are fresh water, fertilizer, arable land etc. renewable)? Is wind renewable?
http://www.earth-syst-dynam.net/2/1/2011/esd-2-1-2011.html
What about hydroelectric (we seem to have run out of rivers to dam)? Is there really agreement on which of these are included? I've been working in the field for five years and I haven't figured it out.