Unless you're cycling across thousands of miles of Siberian tundra, or you're one of those waiting-for-death geezers who have lost all interest in the world, you're going to want to take an occasional day off to be a tourist whenever you get to an interesting city, relic site, national park, or other such attraction. You spent all that effort to get there on a bicycle. You're not going to just ride past without stopping, right?
That said, I've met multiple such geezers on the road who never stop for attractions. Tragic when one gets to the age where all curiosity toward the world is dead. Kudos to them for still being able to cycle at least. The brain is just as important as the body...
Up until now, all of my recent (Since 2009) touring has been while I was employed, thus limiting my time away. During two-week trips, I would usually plan a day off in an interesting place worth doing something other than riding on to the next place. Sometimes, that day off would involve an out and back ride from camp.
During trips of shorter duration, I rarely took days off except on long weekend trips where I stayed in one place for two nights. The “off” day always involved some riding.