I'm trying to get an Eevee so I can get the fire one that Eevee evolves into with the Firestone.
Trophy Garden, after the National Pokedex. Backlot will tell you if there's an Eevee or not. Also, a free one can be received from Bebe in Hearthome City.
Source: Experience and Bulbapedia
You get it at the trophy garden and a man will tell you there is an eevee there someday. I think I found an eevee in hearthome city too.
Source 1 Experience = Source 2
You get one from bebe in hearthome city or at the trophy garden after obtaining the national pokedex