when you do have internet access, check out Big Fish Games. They have online games, but they are also good place to get downloads from and you get to download a one hour trial version of most things before you buy them so you can see if you actually like the game before you pay any money for it. all the games are categorized by type so it's easier to find the kind you like and some of them you can even play online first (in flash version) if you want. They have gobs and gobs of games for PC, but they also have a decent selection for Mac (which is what I have).

I personally like FizzBall (an interesting twist on the games where you break all the bricks), Luxor and Luxor AR (where you're color matching/exploding marbles as they go by in complicated twisting lines), and Zenerchi (color matching in an entirely different way) and Ouba.

If you're into time management and/or strategy games, I've enjoyed both the Chocolatier games, Cake Mania (though the third one with the time travel is kind of dumb--the second one is the best but only the original is available for the Mac), Plantasia, Burger Shop and Garden Dreams. Recyclorama was pretty good, too, but the interface is kind of clunky.

If you want to check out the hidden object games, in my experience, the Mystery Case Files ones are the best.

I don't like shooting/killing games and I haven't played many adventure puzzle solving games so I can't give you a lot of advice there.