"Harajuku is the station next to Shibuya."
渋谷の隣の駅 = the station that is next to Shibuya
渋谷の駅の隣 = next to Shibuya station
The Harajuku station is in the Shibuya area but borders the Harajuku area on one side. The Harajuku station is the next station before/after the Shibuya station on the Yamanote line depending on the direction you are travelling.
So, I'm not entirely sure Duo's sentence means:
The Harajuku station is next to the Shibuya area.
Harajuku is the next station before/after the Shibuya station.
- 渋谷の隣の駅 = [a/the] station next to Shibuya
- 渋谷の駅の隣 = next to Shibuya's station
= Harajuku [Station] is [the] station next to Shibuya [Station].
= Harajuku is [the place/building] next to Shibuya's station.
Your sentence sounds more like you're talking about some building called "Harajuku" (like it's the name of a shop or restaurant) and saying that this building is next door to Shibuya Station's building.
At least this is how I read it anyway. I could be wrong. ^^
It's a bit of a confusing sentence that Duo have chosen anyway. It doesn't really make it completely clear what "next to Shibuya" means exactly.
Shibuya (渋谷区) is a ward of Tokyo. Shibuya is also a district within this ward. Harajuku itself is an area within this ward too. This ward has not just one station but many. One of these stations is Shibuya Station (渋谷駅). Harajuku has not one station but two — Harajuku Station (原宿駅) and Meiji-jingūmae Station (明治神宮前駅). On their respective different railway lines, both of these stations in Harajuku are the very first stop when coming from Shibuya Station.