How to get Eevee

Eevee can be obtained twice in PokeOne.  It can be found once in the Kanto region in Celadon city and once in the Johto region in Ecruteak City.

Celadon City:  Enter the Condos on the side/back hidden entrance on the west side of the building.

Ecruteak City: Talk to Bill on the top floor of the Pokemon Center.  He will give you a quest to go to his house in Goldenrod City where he will give you Eevee.