If that's $280 USD as your preferred budget, then a Radeon 7870 is a great option. It's faster than a 560 Ti and uses similar amounts of power. Their MSRP is $249.99 and you might find a few 7870s below that. The 2GB of VRAM on the 7870 versus 1GB (except for the rarer 2GB 560 Ti models) on the 560 Ti is also a considerable advantage, even at 1080p.
Will a 7870 give me decent FPS on BF3 and such?