Phone would be better solution but internal mic quality poor. So, (given variability I note above) which small directional mics are good?
The MicW i266 works very well on Android phones. Small, pretty good quality, better than the Rode microphones I tried. Not cheap but worth the price I feel.
The recording app I use is Field Rekorder. Takes some time to understand all the settings but then the results are pretty good. It's not free but worth the price: https://play.google.com/store/apps/details?id=de.pfitzinger.rec&hl=de