Does the cost of living get less expensive when you don't own a car?

No, you've got it backwards, a car-free existence is more expensive. I live in Manhattan, so I can tell you how expensive it is to live here. It costs a lot less money to live in some non-walkable place in the midwest and own a car or two.

I also lived in Arlington VA, and it was walkable but much more expensive than most other places in the USA as well, and you still needed a car to drive to work.

For whatever the reason, packing in people so close together that car-free life is feasible also has the effect of raising the price of everything else, and thus we can only conclude that densely populated areas are economically inefficient.

via Half Sigma: It costs more money to live without a car.

Part two here: http://www.halfsigma.com/2009/05/its-less-expensive-to-own-a-car-part-ii.html