I can speak to you from experience here.
What I own is a black Macbook (2.4 GHz Intel Core 2 Duo, 2 GB RAM, 144 MB GMA X3100 Graphics). You'll be happy to know that the handful of games I played ran acceptably on this computer, so I can only assume they'll run exponentially better on your system.
The games I played were:
Call of Duty 4
Call of Duty 2
Quake 4
Torchlight
Civilization 4
Unreal Tournament 2
So, here's how each ran:
(Call of Duty 4)
This one was playable to my surprise. Of course, I had to use minimum settings and intensive scenes did produce lag, but besides that, completely workable. Remember too that my graphics card is very poor. 1024x768
(Call of Duty 2)
I still play that. It works very well, and I see lag maybe 3-5 times throughout the game. All settings on low though. 800x600
(Quake 4)
Played through the campaign several times. Runs well, almost never lags. Settings on low. 1024x768 (A lower resolution grants me even more fluid gameplay, but I do need some sharpness)
(Torchlight)
Best game on this thing. Works perfectly. Settings on high. 1024x768 (Games don't let me run them in 1200x800)
(Civilization 4)
Impossible to play even with all settings on low. It works okay when you first start to build your empire, but when you expand, it lags like a mofo.
(Unreal Tournament 2)
Perfect gameplay. Almost no lag. High to medium to low settings. 1200x800 (I think)
That should give you a good idea. I'm pretty sure you'll be able to play all these games on medium settings, some high, but definitely on low. Also so you know, I tried Quake 4 on a friend's Macbook Pro (9600m + 9400m Nvidia Graphics) with all settings on high to medium; worked perfectly. Mind you, I only played the first level, but that was always the level with the most lag for me (at least the very first part).
If I'm guessing right, youll be able to play Bioshock on low settings. That game is really intensive graphic wise.