As a guy who makes acoustic guitars, vibration of the wood is what I am looking for. Maple is not going to dampen vibrations. Its purpose as the sound post in a violin is to transmit the vibrations to the back of the violin from the bridge and top. In the guitar world, specifically acoustic guitars, I look for light, strong spruce to make a sound board out of. That's the part of an acoustic guitar with the hole in it. It takes the least amount of energy to get that light, stiff spruce to transmit the vibrations of the strings and move the sound board to make sound.
Balsa is good at absorbing vibrations, but not great. The softer a wood is, the more it will absorb vibrations. The harder it is, the more it will transmit vibrations. So the least dense piece of the lightest wood will dampen the most vibration. Foam rubber will absorb vibrations the best, but structurally, it will not make a good guitar, or pinewood derby car. Ipe, the hardest wood I know of, will dampen vibrations the least, but it is heavy and also does not make good guitar sound boards because of its weight. It probably would not make good PWD cars either because it will skew your COG due, again, to its weight.
So, it looks like, unless you can somehow incorporate a vibration absorbing feature in your cars, the type of wood you are looking for is light, and not too soft to hold nails. Pine works well. Fir might also work well. Do any of you guys make cars from 2x4's bought at Home Depot or Lowes? Those are usually pine, fir or spruce depending upon where you live.