You can find Moon Stones in those places -
> Reflection Cave - 1F, south of Battle Girl Hedvig, on top of the small mesa.
Terminus Cave - This one is on B1F and is hidden so use the Dowsing Machine. (Far north side in the gap in the Wall)
Route 18 - Sometimes given if you beat Psychic Inver in an Inverse Battle.
Super Training - By completing Drag Down Hydreigon! minigame.
More info check THIS. - Serebii
Also some info I used is from HERE, thanks to Kawaii Terlor and ƒιzz.
Hope this helps!