As you can see, there are several options available to you.
If you wish to stick with this build, a brand new i5-3470 goes for about $100 on EBay.
Other things to consider:
-> No matter what CPU you get for this motherboard, it will still bottleneck before the GPU does, essentially still limiting your experience in games. More than anything, this will limit your maximum framerate in games, especially at higher resolutions.
-> I would think about getting your RAM up to 16GB. 8GB is OK for most games, but you would see better performance overall with more RAM.
-> Invest in a SSD to boot from. The Samsung 850 Evo is about the best SATA 3.0 SSD you can buy. Booting the Operating System from a SSD will yield far better boot times, and will greatly increase responsiveness across the entire system, including games and applications, updates, etc.
Hope this helps.
EDIT: The Best CPU I could find for your motherboard, which seems to be compatible as well, is the i7-3770K. I don't know much about your motherboard, if it can overclock or not, or even the specific architecture it uses for the CPU, but the i7-3770K is the best Processor for a LGA-1155 CPU socket. A lot of people get a stable overclock to 4.8 GHz without any temperature issues.