As others post, a motor vehicle though potentialy useful is not essiential, and in some cases a cycle might be preferable.

However everyone seems to be assuming a gasoline powered vehicle, would not diesel fuel be a better choice ?

Diesel fuel is much safer to store, and whilst I am not too keen on any fuel cans in a vehicle, diesel is far less of a risk.
Most diesel vehicles get better fuel mileage, thus a greater range from a given size tank.
Most diesel vehicles can in emergency run on kerosene or light heating oil, or cooking oil, which could be very valuable if regular fuel was not available.

For most natural disasters it might be best to stay put, provided of course that you live above flood level, have a strongly constructed home, and keep supplies for at least a week, and preferably for a month or more.

If you fear any release of radiation, then a geiger counter is essiential.
There is otherwise the risk of getting a greater dose stuck in a traffic jam, than would have been received staying indoors.

If you fear any release of toxic or noxious materials, then a good respirator helps to an extent.
Most toxic materials and chemical weapons are heavier than air, therefore in an urban area, the greatest safety might be achieved not by evavuation but by gaining access to the upper floors or roofs of tall buildings.

(makes me glad to work in a deep concrete basement, which is bomb and radiation resistant, but also have access to fresh air 10 floors up in case of any chemical incident)