What's the best GPU for gaming at 1920x1080 around $200?

Your only viable options in the price range are the 7850(~$190), GTX 660(~$210), or 7870(~$230). Personally I would get the GTX 660 because of lower frame latency , adaptive vsync, physx, and 3d vision (though i doubt that last one will apply to you and maybe not physx either).