I've been wanting to watch the Walking Dead series for a while now. I saw it listed on Netflix, but haven't had an opportunity to watch it without the kids, wife, or something else that needed to be done.
Regarding the board game of choice, Chess was the first thing that came to my mind. After a little more consideration with your suggestions, I'm reminded of a board game that I played with as a kid. It was a tin that was similar to having two pie pans put together, so the container was the board for the game you were playing, with a Chinese Checker board on one side and a Chess/Checker board on the other. I'm pretty sure it had marbles, checkers, chess pieces, and may have also had dice inside, although I'm not sure if they were originally part of that set. It was pretty compact though, light weight, not too hard to grab everything together and go... plus considering that chess and checkers are common games, it's much more likely to be able to find some pieces while scavenging to replace anything that was lost or ruined along the way. Seems like a standard deck of cards could be grabbed and thrown into the set too, to make a decent set with lots of options. I know... that's probably cheating as far as the "one game" rule goes, but I'm pretty sure sets like that are still available in some form or another... and if they are like the one I had as a kid, you're not going to get much more compact than that since it would only about the size of a laptop computer and not even weigh as much...