It depends on your motherboard, but given that you already have the FX-8120 you should be able to handle any of the 125W chips.
That being said...you're currently 4th on the hierarchy chart (http://www.tomshardware.com/reviews/cpu-hierarchy,4312.html), so with the minimum 2-tier improvement you need to look for, you're pretty much wanting to get another of the FX-83xx series. Tom's is recommending the FX-8300 as their mid-range AMD CPU pick (http://www.tomshardware.com/reviews/best-cpus,3986.html), & it's only about $110 USD.
Barring that, there's not a whole lot you can do to improve without starting with a new build.