There is only one place to find Eevee in the wild in Pokémon Let's Go, and that's Route 17 to the west of Celadon City. Eevee is a super rare Pokémon, so I suggest using a Lure to attract as many Pokémon as possible, increasing your chance that an Eevee will appear.
It only has a 5% chance to spawn on Route 17. Source
Good luck hunting!