Things that require nothing, just you. At least in the short term. (e.g., it’s ok to think about what question would be worthwhile to ask on Lesswrong.) I myself sometimes have specific questions from my studies and/or practical matters, which are excellent for this purpose. But the supply of these questions usually is much less than the time I have for pondering them.
If I have nothing else to do, I tend to default to meditating. It requires no props, can be done anywhere at all, and is claimed by many to have some interesting and beneficial results if practiced routinely. On the short-term, it helps to calm and focus my mind and body so I can be closer to peak performance for the next thing I need to do.
The process I use for those interstitial moments is to try to identify all components of my current physical and cognitive experience for a given time span (set a timer... or don't) or until I get interrupted by the next thing. I was surprised to learn how useful it is to do "nothing" for a while.
The early conceptual phase of invention can be done just by identifying a problem and pondering ways to solve it. Other kinds of creativity are possible to do entirely in your head in the short term: composing music, outlining novels, etc. But you can lose these if you don't write them down soon enough.
I tend to favor your own approach - think about whatever I'm working on. The solution to not having enough questions is to always keep a question around which is A: hard enough that you're unlikely to solve it during a brief wait, and B: in a state where you can work on it without something to write on. Combining these two is not always easy, so you sometimes need to plan ahead.
Departing a bit from the question as stated, adding a phone(and headphones), I've also found that listening to audiobooks is a good way to use e.g. a commute.
with only your own mind?
Math: I make up problems, often involving (discrete) sequences.* (Being interested in the problem helps.)
Reading.
*Without paper: Geometry:
a) What is the greatest distance in a cube? And what is it's measure? In a tesseract (4-cube)? In the n-th hypercube?
b) What is the area of an equilateral triangle as a function of the length of one of its sides? The distance between the center and the corners? The distance between the center and the center of one of the sides?
With paper:
More general version of b): Consider the sequence of (regular**a) shapes with the least number of points for it's number of dimensions. What is the the hyper volume of the n-th shape as a function of the distance between the center and a corner (it's the same for all corners**b)?
**While I assert a -> b, I haven't proved this from the definition of regular polytopes.
If I have nothing else to do, I tend to default to meditating. It requires no props, can be done anywhere at all, and is claimed by many to have some interesting and beneficial results if practiced routinely. On the short-term, it helps to calm and focus my mind and body so I can be closer to peak performance for the next thing I need to do.
The process I use for those interstitial moments is to try to identify all components of my current physical and cognitive experience for a given time span (set a timer... or don't) or until I get interrupted by the next thing. I was surprised to learn how useful it is to do "nothing" for a while.