"There are many department stores in Shibuya."
This is one of those things where the topic is not clear to me. I thought we were talking about department stores, but it turns out we were talking about Shibuya.
It is needed if "Shibuya" is the topic.
e.g. Your friend asks if she should choose a hotel in Shibuya. Shibuya becomes a topic.
How is this hotel in Shibuya. (The hotel is her topic.)
It is good!
(You respond to her topic.)
Talking about Shibuya, there are many department stores.
(You shifted the focus to Shibuya.)
There are also plenty of delicious restaurants.
(You can continue to talk about this topic)
しぶやには... The answer, には is not wrong, but it's quite unusual only with this sentence. You can simply say しぶやに.
しぶやに たくさんデパートが あります。
... には ... が ... It's to stress expression, and it sounds like:
I have never seen such numbers of department stores! Or, you can't find these kind of many department stores except in Shibuya.
But this sentence is just saying a simple fact, and there are lots of the other towns which have many department stores.
That's what I thought. 渋谷に。。。and we are talking about Department stores, which takes は.
Not in this sentence because a location to exist あります can only be referred to with に. But in other suitable context しぶやでは is also possible. e.g. 渋谷では、常に新しい文化が生まれています。/ In Shibuya, new culture is always being generated.