​​​​​​Keep digging. The Gyoen is the garden within the park. You can see it's just a part of the shrine, on the South side, labeled #20: https://www.meijijingu.or.jp/guide/ It'll cost you JPY 500 to visit.

If you prefer, you can read more about it, right here: https://www.meijijingu.or.jp/midokoro/gyoen/

If that idiotic Google maps led me there, I'd be mostly satisfied. But it's telling me to go to the Sangubashi gate (Sangubashi Station East Exit), when the Harajuku gate (Harajuku Station West Exit) is right next to it. As a matter of fact, that idiotic Google maps makes me walk all the way around the park, in one instance walking by the Yoyogi gate before getting to the Sangubashi gate. You can see this on the Jingu's own website: https://www.meijijingu.or.jp/access/