Really does depend on the church, and on your predilections. You have had some great suggestions here, including: Pay attention (so you actually know what you’re rejecting—and I’ll add, so you can still get a valuable cultural grounding); meditate; read stuff.
I’m grateful I was forced to go, but I got bored a lot too. And this was a Greek Orthodox service, where there’s nothing to read (for free; you can buy a missal, and few do), where the service was in Ancient Greek (I was grateful for it; most aren’t), and where audience participation is rare.
If you won’t get anything out of the service, and you can’t get a reasonably covered up distraction, think about stuff. You’re offline in a place without distractions: that is a valuable thing, don’t waste it.
Plan your next Quora answer or three, for example.