$20,000 can buy a pretty nice and reliable used or new car. Here are some good choices of cars.
New: Jeep Patriot, Jeep Compass, Dodge Dart, Dodge Avenger, Chrysler 200, Fiat 500, Chevy Sonic, Chevy Cruze, Ford Fiesta, Ford Focus, Ford Escape, Toyota Corolla, Honda Civic, Kia Rio, Volkswagen Golf, etc.
Used: Jeep Grand Cherokee, Jeep Wrangler, Jeep Liberty, Dodge Nitro, Dodge Caliber, Chevy Equinox, Ford Edge, Chevy Malibu, Ford Fusion, Ford Taurus, etc.