I only recently began using a smartphone app, mostly for the navigation to minimize wandering around trying to find a new route (not lost, just... meandering). It also records distance, speed, etc., but I don't look at it while I'm riding. The phone is on my belt or in a pocket and I look at the info later.

I still wear an old Timex analog wristwatch but don't look at it often while riding unless I'm trying to catch a bus for part of the trip.