Castle in the Air is indeed a companion to Howl's Moving Castle, but the first thing to accept is that you won't be seeing much of Howl and Sophie. Once I did that, I was able to relax and enjoy this entirely different book.
Abdullah is from Rashpuht, and this is where the story begins. As the names suggest, there's a definite "Arabian Nights" flavor to the narrative. Abdullah finds himself with a magic carpet, that he doesn't know how to control, exactly, and meets with the princess Flowers-in-the-Night. Who is kidnapped right in front of him by an evil djinn. And so Abdullah goes on a quest to rescue his beloved, which eventually brings him to Ingary, and into contact with characters from the previous book.
There's some really fantastic characters in here. Abdullah himself, who is a smooth talker but quite sincere in his love for Flowers-in-the-Night. Flowers-in-the-Night herself, who isn't content to be in distress and who is as intelligent as she is beautiful. And Princess Beatrice in particular, though she isn't in much of the book.
The plot has a traditional fairy tale feel to it, with some twists. It also has the same sort of chaotic ending that Howl's Moving Castle had, which I liked. I'm very eager to continue the series now.