Android - Dropbox for Android folder location
Dropbox 3.0 (3.0.3.2) and Sony Xperia T3:
/Android/data/com.dropbox.android/files
As of Dropbox 2.0 the right location by default is
/mnt/sdcard/Android/data/com.dropbox.android/files/scratch/[files]
Found the things with Astro file manager (Samsung Galaxy Tab 8.9).
Moto G4 [Aaron]
On a new Moto G4 the Dropbox app has no "star" mechanism, instead you enable the "allow offline access" option, and the actual location this file showed up was
/Android/data/com.dropbox.android/files/[userhash]/scratch/[file]
For now in the Dropbox App there is no download option, but there is favorite option (star).
When you favorite something, it downloads this for offline use in sdcard/android/data/com.dropbox.android/files/scratch
You can do it only for files, not whole folders.
Dropbox on my Samsung Note 3 has its storage at /storage/emulated/0/Android/data/com.dropbox.android/
.
HTH