uhm.... I don't think there would be something other than an AMD APU based rig that would fit into that budget. I can be wrong, though, don't just go off my word. But what you can do is just put the money into your savings and just save up more until you have enough to build something around eight hundred to a thousand dollars.
I run an APU system (A10-5800k) and I have had okay ish performance on GTA 4 with just the integrated graphics, but I chose to add a 7770 to the mix and now I am more than happy with performance
Man, save some money up and get a decent rig from teh get go. If you get a good foundation out of the gate, you will be able to easily upgrade for a good long while as you get more money and as the need arises.
I agree with the guy above save more, get something that is slightly forward compatible and playable on better settings it'll make the experience so much better