If we assume that we can ultimately develop a system that is 50% efficient (the best you can do under the Laws of Thermodynamics)
Why would 50% be the most efficient? Surely all the Law of Thermodynamics states is we can't be 100% or more efficient? Or are you treating the solar station as a heat pump; in which case you're right, 50% is the best we would ever get.
and that we are working with an input of 1000 W/mē that is available for an average of 12 hours/day. That implies that, to meet our total energy needs, we would dedicate 2*2*30,000,000,000,000/1000 = 120,000,000,000 mē (or 120,000 kmē) to that generation. That is a square (roughly) 350 km on a side -- and then you have to distribute this power.
The size is easy - there's way more than 350km
2 of Sahara desert, for example, and that is sun-soaked most of the time. As you say, the problem is distribution, not generation.
How about this for an idea - and bear in mind that once the capital costs are accounted for, the running costs would be
comparatively minimal:
1) Use the Spanish "power tower" idea, but scaled up to cover ~350 square kms as you propose. In fact, I'm not sure what the efficiency of the Spanish system is, so let's aim for a 500km
2 system (of course, it doesn't all HAVE to be in the same place; a biggie in the Sahara, one in the Middle East, one in Arizona and one in Central Australia would probably do.
2) Use the energy to extract carbon from the atmosphere, hydrogen from water, to create synthetic oils - all the way from butane through petroleum spirit (gasoline) down to heavy fuel oil, in the proportions which make the most sense from a transportation and electricity generation point of view.
3) Use new and existing rail/road/pipeline infrastructure to transport the product(s) to their destination markets.
Obviously, there are some pretty massive political problems to circumvent there; and a few technological ones; but IMHO it's the easiest way to transport large quantities of energy without requiring expensive cryogenics, pressure vessels, or losing most of it to resistance. It also has the advantage of sucking CO2 out of the air, so the greenists would need to find a new eeevil gas to moan about.
In fact, the biggest immediate problem I can foresee is - what the hell to do with all the oxygen you liberate (2 from each CO2 molecule, and 1 from each water molecule)... sure, some of it could be compressed and bottled, but I'm really not sure about the rest of it...