Your best option is likely a Honda Accord. The Accord Sport handles a little better than the other variants, but might not include other features you want.
Other possibilities include the Toyota Camry SE, Hyundai Sonata, and Subaru Legacy. The Camry SE might ride too firmly for your tastes. The 2015 and up Sonata doesn't have much of a track record, but has been good so far. The Subaru is best if you want all-wheel drive.
If you want something a little larger and more upscale than these cars, the 2015 and up Hyundai Genesis competes with cars like the Mercedes-Benz E-Class, but is within your budget. Like the current Sonata it doesn't have much of a record but has been good so far.