It's true, that motherboard (MoBo) and CPU are really limiting your upgrade choices but you could pick up a Phenom ii x4 965 BE pretty cheap on ebay (just make sure it's the BE as there is another version out there that runs at 145W that might not run on your MoBo). You could then pick up a 7850 2GB and probably stay within your 250 (dollars right?) budget.
I did a very similar upgrade a year or so ago (sorry I'm not trying to rub it in!) and it ran all games (unmodded) at good FPS on high settings. I quickly upgraded again though as I got addicted to modding Skyrim!! My next step (current setup) was a new MoBo and DDR3 RAM.
That should run ok for another year but with the new gen consoles coming out games are going to start demanding a lot more (as they are not optimised for our super powerful PCs) and you'll likely start feeling the pinch towards the end of the year.