I'd look used. IMO, there are no current $500 guns that are accurate, interesting, and pretty. Savage is accurate - I own two - but it's hardly 'pretty,' the finish and design are utilitarian. CZ is an improvement, but still a little disappointing up close when it comes to fit and finish. Again, it's a functional and accurate shooter.
If you're patient, I'd look around the used gun listings; there's lots of really nice bolt actions out there that are both shooters, and have a high level of workmanship. Top of mind at the moment include the Remington rimfires - a 504, 541, or even the Five. Some of the old winchesters are really nice, too - especially the 52, but I doubt you'll ever see one for $500. If accuracy is your thing, the CIL 190's are really re-branded Anschutz rifles, known for accuracy. While not quite benchrest-accurate, the Browning T-Bolt is a fantastically charming bolt gun, wicked fun to shoot, one of my mainstay go-to bolt guns that rarely gets left behind when I go out shootin. Older Mossberg bolt-guns have a cult following out there - I've tried a few of them and never could get too attached, myself.