So you want the cheapest cpu you can get without bottlenecking the 670? I assume when you say bottlenecking you mean not getting comfortable fps because the cpu is so weak.
I think the $79 AMD Athlon x4 750 or $89 x4 760k are the cheapest cpus you could get and still get playable fps.
A $99 FX 4300 will work for sure.
A $119 FX 6300 would be even better and I highly recommend it on a budget.
A $159 FX 8320 is even better for a little more.
I know any i3 will work, but they are not really recommended as they are just dual cores.
i5s start at around $175 and any of them would be great.