The best GPU a 300w PSU can support is the Radoen HD 7750 DDR5 and the GTX 650; the GTX 650 is a little faster. You should be able to buy a HD 7750 DDR5 for around $80 after rebate at Newegg.com; one was selling for as low as $66 with a promo code, but that expired two days ago. The GTX 650 is probably around $90 - $95 after rebate.
If you must go for a Radeon HD 6670 then be sure to get the DDR5 version. The Radeon HD 6670 DDR3 only has 76% the performance of the DDR5 version which means it is slower than the previous generation Radeon HD 5670 by a decent amount.