"Harajuku is the station next to Shibuya."
- 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.