New cpu

I have a gtx 560, (I don't feel like I need more than that for now)
but my cpu is from 2009 (or older?) : intel core 2 quad cpu q8200, 2.33GHz
windows 7 professional 64bit, 6gb ram < not sure if needed here
and I wanna buy a new cpu but I have no idea what, something good enough for gaming

budget, 150$ ~ 250$

anyone?

my super detailed answer

i think she just needs a new cpu,essentially the problem is that we cannot help you without knowing what your motherboards socket is....
haswell cpus use the Z87 Chipset and other cpus use different chip sets so...yea
is it that cpu? Intel Core 2 Quad Q8200 2.33GHz LGA 775 95W Quad-Core Processor BX80580Q8200 - Newegg.com
i guess so,so it looks like it using the LGA 775 socket which is very outdated and ur cpu is 45 nm ,that makes all sense now.
so so get a better cpu u need a better motherboard which may say you might need a diffrent aftermarket cooler(if the case is so) but cpus come with stock fans usually.
mostly id say u need to buy a new computer...i would still use your GTX560 but your computer has gotten to a stage in which you cannot upgrade it any more and its weird how the 560 isnt bottle-necked but that is not 100% surely the case....so
id get a new computer,answer me if u need help in choosing a good one...you have many working parts left as it seems,but u cannot upgrade that cpu. thanks for reading.
thank me if i helped you
greetings Ex0rpl4net