Ran Mouri, definitely! <3 She's Shinichi's childhood friend, after all. And she has a really close relationship with Shinichi. With Haibara, while she may have romantic interest in Shinichi, I don't think that their relationship can grow strong as much as Shinichi's relationship with Ran. Uchida Asami, has only been introduced in two episodes, so I don't see much character development with her. Ayumi's relationship with Conan is very cute, but Conan's feelings for Ran are still with him even when he's small, so Conan only sees Ayumi as a close friend.

About Heiji, he is Shinichi's best friend. Their friendship is a very extraordinary one. They are more like brothers than friends.