Notion of downtime depends on duration of the trip.
For a short duration of a week or less, I'll typically ride most every day. I bring a kindle and get caught up on reading and podcasts. If I am in a more urban area, I'll go out and explore. If camping, I'll have enough chores.
For an intermediate duration of up to two months or so, I'll have occasional rest days. Those happen either because of circumstances (e.g. take a rain day or deal with a mechanical issue) or because I am in an area I want to explore further off the bike. I am definitely keeping a journal of my travels so spend some time updating it.
For a duration of longer than two months, the notion of down time can stretch more into a week or more. It ends up being a bit more focused on circumstances. For example, in an (18-month) trip from Alaska to Argentina, I spent (a) a week in Smithers BC dealing with a broken hub and otherwise exploring Smithers (b) about six weeks after finishing US but prior to entering Mexico to visit Portland, go to Austin for a few weeks and visit family for Thanksgiving before continuing (c) two weeks in Oaxaca attending a language school (d) a week exploring Panama City (e) two week visit between North and South America to also do my taxes (f) two weeks exploring Mendoza, Argentina (g) a week visit back to see family in the US (h) four weeks attending language school in Bariloche (i) a week and a half exploring Puerto Montt (j) almost a week in Ushuaia to explore the end of the world. So I was breaking up a year and a half tour with some variety along the way that wasn't always cycling every day.