Any car are above average for their safety. If you want excellent safety, then the price will be higher.
Moreover, whether you are only looking for new car, or used car. Few years old used car can safe your several thousdands as well.
Japanese and European car's reliability are better than US brand. So look towards this area.
I highly recommend to take "preventive driving" lesson for those who think they are average driver, and unsafe in certain percentage. Learn the safe protection skill, and cover yourself, child, as well as whole family. I mean driving wild and crazy does not mean it is unsafe.
Following are some recommendation for any of their model
Honda, Toyota, Audi, Acura, Lexus, BMW, Merc Benz, Nissan.
If like sport and drive wild
BMW Z4, Mazda MX5, Honda S2000, Lexus IS350, Merc Benz SLK, Nissan 350Z
Korean car are safe and reliable for first 5 years. So if you can specify some criteria, it will be easier for other to recommend.