I'm assuming you're talking about a GPU here, since you're in this section, and for what you want, this is about the best "cheapest" option for you.
MSI GTX 560 Ti http://www.newegg.com/Product/Product.aspx?Item=N82E16814127616
$219.99 ($199.99 after MIR)
You can also go with this, but you'll have to use lower than Ultra quality settings in BF3 at 1080p. It's a good card that I can personally vouch for since I have one, it just won't do Ultra quality at 1080p in BF3 (with decent FPS).
Asus GTX 560 DCII OC http://www.newegg.com/Product/Product.aspx?Item=N82E16814121446
$179.99 ($159.99 after MIR)