The closest thing to the Walled City is an enormous recreation of the Walled City in a gaming arcade (!) in Kawasaki, an unprepossessing suburb of Tokyo. Here's a blog post with lots of pictures. Address ウェアハウス川崎 (Warehouse Kawasaki-ten), 川崎区日進町３−７, official site (Japanese only).
More authentic if rather less exciting are a series of walled villages in Hong Kong itself, of which Kat Hing Wai is the largest and best known. However, while packed, they're pretty low-rise and not all that exciting.
The final alternative would be the infamous Chungking Mansions of Chungking Express fame, right in the middle of Kowloon and not all that far from the site of the Walled City. It's a single building, but a very large one, and like the Walled City it's crammed full of shops, guest houses (hostels), cramped apartments, shady characters, questionable hygiene, total lack of fire safety etc. However, it's also very popular with backpackers (because it's cheap!) and generally pretty safe if you keep your wits about you. See official(?) site and a nice BBC story.