I'm with Eximo's suggestion to overclock. The best CPU upgrade you can pull is an i7-860, which only gives you a slight clock speed increase and hyper-threading. The latter offers very little to gaming and the former can likely be matched by an OC on your current CPU. It's always a bit of a risk going second hand, you never know if you get something that's been heavily OC'd for years.
My suggestion is to get a good CPU cooler that's compatible with both your current chipset and the new Intel chipset... most should be. That should get you a little longer out of your current build and then you can re-use the cooler if you decide to upgrade later.
People treat a CPU bottleneck as if it's a terrible thing. While it means for some games you could have bought a cheaper GPU and got the same performance (BF4 multi-player is definitely in this category), there's plenty of other games, like Tomb Raider for example, that aren't really affected by CPU at all (within reason of course!) Naturally in a perfect world it'll never happen, but as long as you're aware that some games your CPU won't allow the GPU to fully stretch it's legs and can still justify the investment, it's still a good purchase. Without doubt you'll get a better experience over your current 560ti that's for sure.