Just one person? And aside from pleasantly passing the time with random chatter...

Squash.

Loved playing squash with someone of similar ability, just socially keeping score in a endless game until we're too tired to play.

Thinking of nothing else for a time, focused on the game.

Sadly my health hasn't been up to that for a while now... But that was great.

As a group activity. Table-top RPG with long-running worlds.

Usually D&D but even system-less story-teller games. Whether running the game or playing it.

Role-playing with an experienced and familiar group of friends that can flip instantly in and out of character to chat about the game as much as play it - that's great fun. We could do that all day (and in some instances most of the night)...