I've just started doing a NYT crossword puzzle. Seems like just the right amount of challenge, involves some lateral thinking, has a neatly defined end, and only takes about 20 minutes.
I do the daily mini crossword on the Times crossword app with my morning coffee. I try beat it in under a minute (21 seconds is my personal record). It's not particularly challenging, but I treat it like morning stretches for the mind, it definitely helps get the brain warmed up.