Suppose that you were responsible for choosing the target for a new "Manhattan Project" for the United States. For those who don't remember, the Manhattan Project was the top-secret effort to build the first atomic bomb. The effort cost, in 2012 dollars, about $25 billion. Actual development and production of the weapons was surprisingly cheap; 90% of the money was spent to build and operate the factories that produced the necessary fissionable materials (highly-enriched uranium and plutonium). Another way of measuring the size of the budget is that the total amounted to about 16 months worth of NASA's current budget.
In setting some parameters for the project, it is useful to ask why the Manhattan Project was successful. My personal opinions on that matter are that the project avoided all of the principle reasons that tech projects often fail. It wasn't vague: the goal was to produce a working atomic weapon small enough to be delivered by the bombers of the day. There was a reasonable chance of success: soon after the project was organized, the until-then-hypothetical sustained nuclear chain reaction was demonstrated. It had a challenging schedule: it was believed at the time that Germany had a well-developed nuclear weapons program, and that failure to be the first to have a working weapon could mean losing WWII. And finally, it was publicly funded so the participants were focused on solving the problems: no one was distracted by thoughts of how the project would make them rich.
Let me take those as the parameters, then. $25 billion total budget; specific "product" to be delivered (quantity one, or at most a handful); and broadly useful in the sense that it's produced new knowledge about how to build something. I'm mostly an energy guy these days, and a macro- and supply-side energy guy at that. And I'm concerned with the electricity part of the problem. I believe that it is straightforward (which is not to say easy or painless) to cope with the liquid-fuels issue, but I am much more concerned about keeping the lights on reliably. I have three possibilities on my short list. To cut off arguments, I'll point out that using the money to build out transmission capacity, or to put up 10,000 wind turbines, doesn't satisfy the criteria.
First possibility -- a 500 MW or larger generating station based on solid carbon fuel cells, operating at high efficiencies and reproducible at reasonable cost. There are a number of possible fuel cell technologies that are at least laboratory toys, eg molten-tin-anode cells. The US has massive coal reserves. It seems probable that much of those reserves will eventually be oxidized. Fuel cells operating at high efficiencies, relatively low temperatures, and producing a nearly-pure CO2 stream that could more easily be sequestered seems like a better alternative than what we currently have. Ideally, such fuel cells should also be able to accept suitably dry biomass, high-carbon waste, or other sources of carbon.
Second possibility -- a modular factory-built high-burnup fission reactor. Ship it to the site, hook it up the the steam (or gas) turbine system, let it generate electricity for 15 or so years and then ship it back to the factory for refueling, refurbishing, or whatever. I know that fission is controversial, but it is my belief that at some point, the eastern US will once again embrace it. A large majority of the US population lives in the states of the Eastern Interconnect, an area that is relatively low in renewable options. As their existing generating capacity (almost 70% of which is coal and nuclear) ages and is retired, a significant fraction of it will have to be replaced. It seems almost a sure thing to me that fission will continue to have a sizable piece of the pie.
Third and final possibility on my list -- high-capacity batteries for traction (and some fixed) applications that use non-exotic materials (given global supplies, lithium is becoming an exotic material). The battery doesn't have to be perfect. For example, I don't care if it can't be fully recharged in minutes. People will learn to live with such limits. Much of the money may be spent figuring out how to manufacture necessary materials. There are several intriguing possibilities for battery/capacitor/combination tech using graphene and other carbon structures. The problems with those are figuring out to produce the right nanostructures in volume and at a reasonable price.