I understand that this is cutting it close to the $200 mark, but both a 7870 and 660 will beat up a 560TI and steal it's lunch money, and draw less power on top of it all.
HD 7870 ($194.99 after rebate) http://www.newegg.com/Product/Product.aspx?Item=N82E16814202010
GTX 660 ($194.99 after rebate) http://www.newegg.com/Product/Product.aspx?Item=N82E16814121660
Not that the 560TI is a bad card. Certainly not at $150. The newest gen just has it beat the same way it happens every year.
A good place to check out benchmarks is generally review sites, looking for the most recently released GPU, as that will have the newest drivers at the time.
While the review itself is about the new card, that isn't what you're looking for. The Benchmarks pages should have numbers from all recent GPUs, at least in that price range, and give you an idea where things are in comparison to one another. After that, you go price hunting, and balance performance and what you're willing to spend.
In this case, the GTX 660 is the most recent card in this price range, and is a good enough place to start;
These are not all the review sites, not even close, but it's a good number of reliable ones. Don't forget to go the the next page, there's a lot of things they cover in each review.