I see HD7870 as the best price over performance for that price range...
but..
The thing is..I think you should already consider to upgrade your rig...I mean...completely...not just the GPU
E5200 was not exactly the highlight back then 5-7 years ago and is definitely not anymore today.
I already moved from my 6 years old Q6600 to 3770k...and my Q6600 was already way better than E5200...
Any new GPUs will be bottlenecked by your E5200.
Try to consider doing big revamping
...that will definitely need more than USD250 of course..
Edit:
Bioshock Infinite and Crysis 3 are the games which somehow encouraged me tremendously to ditch my Q6600 and get i7 3770k.
Edit:
I did not have any problems with Skyrim, ME3, Torchlight 2, Tropico 4 and Starcraft on Q6600.
I just had some small issues with the newest high-tech games...on Q6600 of course...
Now..waiting for the HD88xx