I believe that the APUs use a different socket than all the other classes of CPU (which use socket AM2/AM3/AM3+) that AMD offers. Maybe an A10 series CPU, but the increase in performance probably isn't very much, I have to check to be sure. Since the APU die dedicates so much space to graphics instead of (CPU) processing power unlike any other CPU, their per-core and overall performance (as a CPU) is noticeably weaker.
The APU series CPUs are usually recommended by people as a good setup for playable to decent gaming if you're on a very, very tight budget. Some of the fastest models are cheaper than even the Core i3. It's integrated GPU is the best on the market, so the extra cost of a graphics card is eliminated, thus saving you an additional $150+. But if you want to seriously upgrade your CPU, you'll need an AM3+ socket board to get any better CPUs from AMD. Just take a look at how much the FX-8350 crushes one of the fastest A10s on the market:
http://cpuboss.com/cpus/AMD-FX-8350-vs-AMD-A10-7850K
So at this point, if you have the money (yes, I know it'll cost you more, but you really don't have many options), you have to replace your motherboard. Take it as an opportunity to enjoy better platforms. Perhaps you might want to get an i5 or stay on the cheaper side of things and get an FX-6300. But if you do, you'll need a graphics card too. The integrated graphics on these CPUs are far weaker than your APU.
Want an even cheaper way to boost performance? Just buy only the graphics card. Sorry, I know this message is a bit long and winded, but you asked about better CPUs, and I gave you an explanation about better CPUs.