Where to find Gastrodon in Sun, Moon, Ultra Sun & Ultra Moon

SOS Encounter: Ancient Poni Path, Exeggutor Island, Poni Wilds + 1 more
Walk: Ancient Poni Path (10%), Exeggutor Island (10%), Poni Wilds (10%)
Surf: Poni Wilds (20%, Only in Sun & Moon), Ancient Poni Path (20%, Only in Ultra Sun & Ultra Moon), Poni Breaker Coast (20%, Only in Ultra Sun & Ultra Moon)

Gastrodon also appears in

How to get Gastrodon in Sun, Moon, Ultra Sun & Ultra Moon

Its base catch rate is 75 out of 255 (higher is easier); the catch rate calculator works out your odds with each ball.

Evolution: Shellos → Gastrodon (Level 30).

Gastrodon in every game · Pokémon Sun, Moon, Ultra Sun & Ultra Moon interactive map (Alola)