The 560Ti has almost the same performance as the 470. The 470 runs much hotter, but if that doesn't bother you then upgrading doesn't make sense. Check out this comparison
of 470 vs 560Ti. This comparison
between the 470 and the 6950 shows the 6950 being slightly better than the 470, by more of a difference than the 560Ti over the 470. The 6970 is a fairly significantly better card than the 470.
My recommendation to you: If you really want to upgrade your GPu, look up threads on how to unlock 6950's into 6970's and pick up one of the ones with higher success rates. That way, you have a card better than a 560Ti anyway and then you have a good chance of having a truly worthwhile upgrade.
If you're not dead-set on a GPU upgrade, put the $250 into a WC loop if you want to tinker....or an SSD if you REALLY want a performance boost, a new CPU/cpu cooler, more/faster ram (don't go over 8GB@1600, no real need). Honestly, your GTX470 is an awesome GPU...and you can do a much better job of gaining a noticeable performance boost for $250.