[LINK] Runner's World
Only concrete is worse than asphalt for a running surface, and not by much.
By using the shoe selector at Runner's World, and selecting the Cushioning criteria, you can find the top 30-35 shoes (in varying price ranges) which minimize the damage.
Pick three in your desired price range which are rated at 4-5 stars by other runners, and click on "compare" to compare them.
If you have "issues" such as pronation, you'll need to select the option for shoes with more control.
Technically speaking, you should use shoes with cushioning for training, and racing "flats" for the actual race. But, since the Dumpster Dash is not exactly the Olympics, I'd just run it in the training shoes to minimize the risk of injury.