The caption/description field?
And all your processing will be visible by switching to the develop module.
I had avoided "Caption" because I knew it was used in other modules, such as Print and Slideshow, for display alongside the image, which is not what I want. "Description" sounded like a better choice - until I discovered that "Caption" and "Description" are just two names for the same field - if I type something into "Caption", the same text appears in the IPTC "Description" field (and vice-versa).
So I guess the answer to my question is: No, there is no specific facility for making private notes on an image, but in a pinch you could use the "Caption" field - as long as you don't want to have a real caption for your image.
Re "all your processing will be visible by switching to the develop module" - yes, I realize the History panel shows what you've done, but I would much prefer to read something like "Accentuated the colors in the scarf" than to interpret "Add Brush Stroke" (repeated 29 times). And that's assuming, of course, that you haven't at some point cleared the history information, in which case it is all lost.