If you insist on upgrading something, replace the GPU. You should be able to get an overclockable 7850 in your price range, but be mindful that your PSU will need to be able to support it, and it still won't allow you to steadily hit 60+ at highest settings.
Your best upgrade would actually be to replace the CPU, but that would require also replacing the MoBo, which would cost you at least $300-350.