I'm currently playing through
Stone Age which is a puzzle game. Get your guy to the exit within a set time. There's probably trained ADF's if you just want a straight puzzle game without time.
Push-Over,
Chips Challenge and other puzzlers sound like they'd be great for what you want since they can be played with just a joystick, don't require amazing reflexes, and I believe all have level passwords so you can pick up where you left off later.