I'm going to second the turn based suggestion. How about a nice 4X game? Galactic Civilizations II is pretty easy to get into, being basically Civilization 2 in space and in a format that works on modern computers. There's also the actual Civ series. I wouldn't recommend any of the more complicated 4X games if you're looking for something relaxing and simple; a lot of them are pretty much Spreadsheets: the Game, which is good if you're into it, but even then you have to be serious about it to decide to sit down and play a situation.
Edit: Shoot, Missed the PS3 part. I don't have a PS3, so there's nothing turn based for it that I can personally recommend, but I will note that the two series I mentioned have entries that will run on pretty much any computer capable of accessing the internet. Basically, if you can use Facebook, you can run GalCiv and Civ III and IV.