Yes it would be. But that doesn't matter if no humans make it through the apocalypse in the first place.

The moon would do the job at a lot cheaper price.

Nope. Because of aero braking, Mars takes less delta v to get to and land on than the moon does.

Now I'm wondering why the Apollo program went to the moon if doing Mars is so much cheaper.

Going is cheaper. Coming back is more expensive. And of course the 3-6 month travel time is a challenge.