I don't think fully-electric cars are too far off, and when that is the case, the nuclear energy will be able to power the cars directly (or at least their batteries), along with solar power or whatever else.
Electricity is simply much more flexible since it can be produced and used in so many ways and distributed relatively cheaply. Gasoline only works for combustion engines, and it has to be manually transported. Our current infatuation with gasoline is going to look pretty stupid when we finally get to the point that it's hardly used anymore.