The 6600GT is below the minimum specs for Mafia II. The 8600 GT is listed as the minimum requirement. Minimum usually means you'll barely crank out 30FPS at the lowest settings at a low resolution. The 6600GT is considerably slower than the 8600GT, so that's why you are getting horrible performance.
The PhysX option for Mafia II is in the graphics options of the game, it's called APEX Physics or something like that.
In any case, you need a new video card if you want to play any modern titles. The 6600GT just doesn't cut it for most games released in the past 3 or 4 years. At this point there are integrated graphics chips out there that are considerably faster than your current video card.