Yes 6670 is a good choice. But it will not give very good performance like 6850 or better. If you can upgrade your PSU and stretch your budget to $200 for PSU and GPU, I recommend changing to 6850 instead of 6670.
Well they should run in medium Setting I think (at 720p). They are not games like BF3 or metro 2033 which is the most demanding game in the planet. And if you are asking about the Nvidia counterpart you it's maybe GT 440 or GTS 450.