Eevee can be obtained once in Kanto and Johto.
(Kanto) Celadon City: Enter the Condos on the side/back hidden entrance on the west side of the building. Then go all the way to the top floor and Eevee is in the Pokeball.
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.
Eevee can also be found in the grass and dark grass in Castelia City Park in the Unova region as a rare spawn.