So my build has been surprisingly solid for the games I play, but lately I've been seeing it have a little harder of a time running much more demanding games like Far Cry 3 with any more than 15 FPS, give or take.
So I was wondering if it'd be more important for me to invest in a <$200 graphics card (preferably NVIDIA), or <$200 processor.
IF you upgrade your Cpu, you'll need to completely ditch that setup. Time for new motherboard/ram/cpu in fact. I'd wait for a combo deal from Newegg where you buy a motherboard and get ram free, that'll save you some money, and get all three at once.
If you spend that much on a graphics card, with your current setup you'll be bottlenecking it. That's fine, because when you finally do upgrade your cpu(ram and motherboard) you'll get the full benefit from it. If you can swing it, I'd buy an nVidia 760. It generally runs about 250-260 dollars though, but at that price point nothing really touches it.