I found out Neil Gaiman when I read American Gods, which I enjoyed much more than the TV series based on it. Also a book about a parallel magical world that most people are not aware of, it was still something I felt was very American, very Western, even if it was telling the stories of a multitude of gods from all over.
Neverwhere feels more like Spirited Away than a Western story, though. And it is funny, because the mythology used as its base is British and everything happens in a parallel underground London. The lead character is an anonymous successful dolt working in the financial system who is suddenly thrust into this magical world by a simple act of kindness.
The book is rather short and the story, while extremely enjoyable and very well written, is not that important. I mean, it's a classic hero journey (I am a sucker for those) but the beauty is in the characters and the details. I still would have wanted the main character to do something about Anastaesia and the reasons why Door was alive, then people trying to kill her, then back again are quite dodgy when you think about it. Also, the Warrior? Seriously?
Bottom line: if you feel like immersing yourself into a magical world that feels close and real, but also incredible and impossible, then that's the book for you.