My first thought was that I'd play something addictive that I've played a lot before, in my case Civilization (or other turn-based strategy like Master of Orion). Sims also goes to that category and all kinds of sandboxing would be a step away from serious gaming.
On the other hand there are couple go-to genres for me. For couple decades I've been saying that when I "have nothing to play" (a feeling much more rare today than twenty years ago), I play old JRPGs. Because they're a genre often so generic they're easy to get into (but it's still satisfying to find interesting twist in them). Or old point'n'click adventures, a light easy thing to play (90's style, not 80's).
And most of this fits to idea that you can watch TV or do something else while playing. You don't have to be concentrating in the game, just playing a little bit on the side of doing other things. We can argue whether multi-tasking is good for you, bit it's one thing to try when out of energy for hardcore gaming.
Also: Angry Birds. Puzzle games in general, but physics based may be the best option.











