Hmm,

If some major event happens, you can figure that public transport is pretty much outta the question. As stated, they will be iffy at best. Since this includes freighting services as well, you can also forget about "shipping yourself" somewhere. Fuel prices are going to be insane, so $250 might only get you one tank of gas, if that. Striking out afoot or on a bicycle really is not an option (uh, the middle of the desert, not practical).

With $250 and a car, you could try and parlay to get something different, but anything that would seriously help you out isn't likely. You could get a gun and try stealing your way to Chicago I suppose.

If it were me, I'd try and head south. You got some serious desert in all directions, but I think I would push for Pheonix, Flagstaff or at least Kingman if I had to go anywhere. I would not try to go to LA, and I think the others are just out of the question.