yea, trophy garden is the way to go. use this little trick:
after getting the national dex, go to the first room on the right in the building with the trophy garden, you will find mr backlot in this room.
before speaking to him, save the game. then speak to him, answer "Yes" every time he asks you if your envious. he will then say which pokemon he see in the trophy garden, if he says eevee then brilliant, you can go catch eevees in the trophy garden, if not turn off your game, then turn it back on, you will be where you last saved, talk to him again and he will go through hte same things again.
keep doing t his until he says "eevee".
you can only do this once a day, you can also get porygon and minun/plusle here, aswell as others