What kind of safety are you looking for?
Do you want a vehicle that when you hit a brick wall or anything else you destroy whatever that is and drive away unharmed? or do you want a vehicle that you are less likely to get in an accident in the first place while driving?
About ten years back I read about a study that listed a number of vehicles that had the highest number of deaths per 10,000 vehicles on the road and the vehicles that had the lowest number of deaths, these included hitting pedestrians, single vehicle accidents, anything where someone was killed because of a vehicle and it showed a trend of larger vehicles killing more people then smaller vehicles, I would really like to find more studies like that but as of yet I have not had any luck.
Forbes also published a list of the 20 safest compact cars that are under $20,000
Chevrolet Cruze - Jim Gorzelany - Forbes and I was quite impressed with what is on there, another vehicle that is no on there is the Chevy Volt, it's not under $20,000 but if you are looking at a new vehicle you can get a 3 year lease for $200 per month! and the option to buy at the end of that is pretty reasonable as well, mostly because the leasing company takes the $7,500 tax credit (not everyone makes enough money to owe $7,500 in taxes) and they I'm sure are getting other brakes as well, so it's almost cheaper to go that route and you get a plug in car hybrid that is based off the Chevy Cruze, both vehicles have great safety ratings but from a car payment point of view and a over all cost of ownership point of view, the volt is a cheap new car to own.