Imagine you could pry off the back of Wes Anderson’s head as if it were a vintage TV set and rummage around inside. What would you find there? A mind like a junk drawer crammed with kite string, Swiss Army knives and remote-controlled toys, or one that springs open as neatly as a well-organized tackle box? A memory palace assembled ad hoc from brownstone apartments, underground caves and submarine compartments, or a diligently designed, continuously flowing and elegant old Alpine resort?

It is this mountain getaway structure that is suggested by Mr. Anderson’s new movie, “The Grand Budapest Hotel,” and not just by its title.

Written by Mr. Anderson, the idiosyncratic 44-year-old filmmaker of “The Royal Tenenbaums” and “Moonrise Kingdom,” from a story by him and Hugo Guinness, “The Grand Budapest Hotel” is the tale of a finicky but charismatic concierge named Gustave H. (played by Ralph Fiennes) in the fictional European nation Zubrowka, and a comic caper he shares with a lobby boy (Tony Revolori) in the early 1930s.

Like the hotel of its title, this movie is filled with Mr. Anderson’s distinctive and pored-over touches: pastel color schemes, baroque costumes and delicate pastries that mark it as one of his films.