Both the CPU and the GPU are your problem. Below is a CPU performance chart with a GTX 680 graphics card (pretty powerful). Your Athlon II X2 250 is a bit slower than the Athlon II X2 265 CPU which is at the bottom of the chart.
This is the CPU performance chart with a Radeon HD 7970 (another pretty powerful GPU) for Hitman Absolution which is another game that is dependent on the CPU and GPU.
there is absolutely no way a 6670 will run crysis 3 (maybe BARELY at the lowest possible settings). I would get a 7790 or 7850 if you want to run crysis 3 or hitman at any reasonable settings.
on a side note, what is the resolution of your monitor? I was assuming 1920 by 1080, but if it's lower resolution, you can get away with a lower tier graphics card
Sadly Crysis 3 is a very demanding game; both CPU and GPU. The below benchmark is at 1280x800 high graphics detail and 2x anti-aliasing. The test rig uses an Intel Core i7-3770k @ 4.6HGz. A slower CPU will result in even lower FPS.
In comparison to the Radeon HD 7790, the Radeon HD 6670 DDR5 performance is only about 45% of the HD 7790. The HD 7790 gets 30 FPS, so 45% of that is 13 FPS and remember that is with a Core i7-3770k @ 4.GHz for a game that is known to be CPU dependent.
Hitman Absolution performance is also dependent on both CPU and GPU. But is not quite as demanding as Crysis 3. The below performance chart shows that a Radeon HD 7790 can get 49 FPS so 45% means about 22 FPS for the Radeon HD 6670 DDR5 GPU with an i7-3770k @ 4.6GHz.
Naturally, lowering the graphics quality and turning off AA will result in better performance.
Both the CPU and the GPU are your problem. Below is a CPU performance chart with a GTX 680 graphics card (pretty powerful). Your Athlon II X2 250 is a bit slower than the Athlon II X2 265 CPU which is at the bottom of the chart.
This is the CPU performance chart with a Radeon HD 7970 (another pretty powerful GPU) for Hitman Absolution which is another game that is dependent on the CPU and GPU.
HD 6670 is a good low end card.
yes it can run Crysis 3 on medium settings(720p) if paired with a good CPU.Hitman Absolution an High settings and 720p. But I recommend you to get a better card like atleast a HD7770.