The best recommendation I can give is an Intel i3-2120 + Radeon 6850. The 6850 is about 80 dollars more than the 6670 but it will mop the floor with Skyrim at 1080p with HD textures installed. It's probably the best bang for your buck right now.
500 dollars is a bit limiting. If you can come up with another $100 to $200 or so you'll be able to get something that will last longer and be more enjoyable. Keep in mind that this is something that you're probably going to have for several years. If you keep the PC for 4 years, then $200 dollars now is just $50 per year when amortized.