I previously ran it on my Core2Quad@2.33Ghz with a GTS250 (1gb). It was able to 'run', but I wasn't happy with merely 'running' the game! Then I upgraded the CPU to an i5 760i(2.8 Ghz) and kept the 250. There was a lot of difference. Only exception, since my GPU wasn't up to the mark for GTA4, I had to tone down the settings a bit (draw distance, etc).
Now, with an i5 coupled with a 470 and 8 gb DDR3 RAM, it's 'almost' flawless!
Point being:
The game ran on both quad core's but is performing better on the i5. True, a good GPU would definitely help, but the game seems to demand more from a CPU than a GPU.
Conclusion:
Your priority should be on upgrading the CPU to a quad core (i5 2500k OR AMD Phenom IIx4). Since your resolution isn't that high, I'm certain your existing card should manage to run the game decent;y well. If not, THEN consider upgrading to at least a 5770. But first, run it for a while after upgrading the CPU.