This is for the Game Pokemon White 2.
Eevee can be found in Castelia City Empty Lot. You first go into the Sewers in Castelia City, head toward the Northwest corner of the room, go up the stairs.
NOT the stairs as far as you can go, but the stairs that immediantly follow up into another passageway of stairs! This will bring you to the Castelia City Empty lot.
There will be a ring of grass, where Pokemon will be found. There will be a tree in the middle. A guy will also be there. Feel free to talk to him, he will NOT challenge you.
He says something along the lines of: "Supposedly, this is where it all satrted for Castelia City." There will be tall buisness buildings on all sides of the Empty Lot.
Eevee, in this location, may be considered rare. But, this game is quite valuable, for in some of the other games you only were given acces to one or two possible Eevees, and you would need a boy and a girl to breed more in those games.
So when you see one, dont hesitate to catch it.
NOTE: you may come upon a skitty. Catch this on eand the next few, but Eevee's are much rarer than this Pokemon!
Another location of Eevee (supposedly), is Amanita. Amanita is on the 3rd floor of a building in Castelia City.
Pokemon to come equipped with:
Eevee is a normal type, so no fighting types!
I hope this helps!
MEMO: POKEMON DAYCARE FOR BOTH POKEMON WHITE VERSION 2 AND POKEMON BLACK VERSION 2 ARE LOCATED ON ROUTE 3.