Lets assume that the apocalypse involves a lot of explosions, leaving behind a generally derelict planet. Without generic equipment, well need a creative person that can build anything from piles of rubbish. Come on down, Dr Brown! Necessity is the mother of invention, and just imagine what Doc Brown could invent in the face of so much necessity. Its exciting just to contemplate. He would need to start with E.T.s communicator, but given that some kids managed to build one in the movie, I'm pretty confident it wont be beyond Doc Brown. Transport? Labour saving devices? Firing the internet back up? All of these things are possibilities. And if he can bring his time machine, I suspect well all be pretty happy.