There are very few quiet cars in the compact and smaller range. To get decent sound suppression, a mid size car is a good choice. From my experience, a Ford Fusion, a Toyota Camry or Mazda 6 are good choices. The Chevrlot Malibu is quiet as well. Avoid Hondas; even the Accord is a relatively noisy car.
The most quiet for the money would be a used Chevy Impala; they go for $12,000 or so coming off lease, fully loaded. The Crown Victoria Ford used to fill that role, but there not many around anymore.
Also, any minivan or SUV is noisier than an equivalent mid or full size car.