I upgraded to an Nvidia 660 OC 2GB, but Bioshock infinite worked fine with old 645 OEM card, and I really can't tell the difference.
I had to disable Secure boot in the BIOS to get my computer to boot up with the 660.
My power supply is at it's limits now, and I ordered a 700 watt supply, because I want to put in a second 1 Tb HD, and a 240 Gb SSD.
I don't know a lot about the 660 TI, but you can get a remanufactured 660 OC 2 GB for around $160, and probably not that much difference.
A 660 TI is probably going to cost around $240, and you don't need it for Bioshock infinite, the 645 works fine.
If your computer has the 635 GPU, I can send you my old 645, you only pay shipping, probably cost you around $8-10.
You really don't need to go nuts on a GPU to play Bioshock infinite, and you definitely don't need a 770 or 780.
Just post here if you have the 635, if you have the 645 you are in good shape.