If you enjoy computer programming then codefights.com is a fun site. You used to be able to challenge other players one-on-one, but I think they removed that feature

But it still has plenty of single-player challenges, and tournaments too.
I also liked the
Professor Layton series for the Nintendo DS/3DS. If you're not familiar with that, it's basically a ton of puzzle mini-games, and then the main game has got aesthetics and an interesting story (sort of a mystery/drama). I don't know how many
Professor Layton games have been released at this point... I played the first 4 or 5 of them but haven't played any of the newer ones.