How good is the public transportation in the city you are moving to? Will you have to pay to keep your car in a garage/space, etc...? If public transportation is good, then you can sell it. If its like what we have here in Phoenix, then bleh... might as well keep the car and your sanity.
Agreed. If you have space and the means to keep the car around, it's not a bad thing to have, especially since you've paid it off. Just make sure that you drive it *sometimes* at least to get the most for whatever you paying on insurance LOL. But in some places it does turn out to be handy. I think this is less of a question of Mustachianism and more of a question of Minimalism - a hardcore minimalist (but not necessarily a Mustachian) would say "ditch the car and bike FOR LIFE!"
And if the bumper is not bothering you or causing further potential damage down the road, I would just leave it as is. Maybe look into DIY painting yourself if you have time. Renting out the car is another great option lbmustache suggested.
Otherwise, if you're moving to an area where it's way more expensive to keep the car, then maybe get rid of it.