GIMP Version: 2.10.6
Operating System: Windows
OS Version: Win 7 Pro
GIMP Experience: Basic Level

List any relevant plug-ins or scripts:
None

List any ERROR messages you received:
None

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How can I change the font size for the program itself (dialog windows, not the text blocks for my projects)? I've looked through all of the program settings and haven't found any place to change it.

You need an editor like, Notepad. Or better yet download the a better editor "Notepad++":https://notepad-plus-plus.org/

Now, find the "Theme gtkrc", depending on what theme you have. The Dark theme is one of the default theme in Gimp 2.10 and you"ll find it on the directory: C:\Program Files\GIMP 2\share\gimp\2.0\themes\Dark. Find the gtkrc and open the file on the editor. Just change the default font number to a higher or lower accordingly to you preferences. Example below.

That worked, thanks!

I wonder why there is no option to change that from within the Settings dialog.

Because it rarely make sense to change only that. You often want to change icon sizes and the like, which is why you can change a whole "Theme" from the Preferences.

And IMHO even though useful, Pocholo's answer is misguided, because:

- you have changed a standard theme, and some future update of Gimp could overwrite it.
- if you share the computer with someone else, that person will have to share your font preference
- you are less likely to backup such changes since they aren't where you keep your data

The right way is to create your own theme (possibly by copying a standard one in the "themes" directory in your Gimp user profile) and then tweak it to your heart's desire, and activate it thought the Preferences.