GTX 560 or if you can find one anymore Maybe a GTX 465. Also if you have the power supply to handle it and can find a deal on them(I have seen them go as low as 189.99). a GTX 560 ti will do nicely. If you want AMD then either a 6870 or maybe....a 6850 can handle 1080. I know the 6870 can.
I can't agree with the GTX 465 recommendation. A GTX 460 1GB 256-bits 336 cores, would be a better idea. Easier to SLI in the future if needed too (easier to find).
Stick to GTX 560, it's cheaper than GTX 460 and GTX 465 btw... With rebate, as low as $155,00 at newegg
6870 - as low as $145,00 with Dirt 3..
Conclusion: Go with GTX 560 or the 6870, don't bother about slower cards..