For history & culture, Ghibli Park (near Nagoya) is hit or miss.
Much bigger than the Mitaka museum, with walk-through recreations of film sets and areas you can lose hours in — a dream for serious Ghibli fans. The catch is huge: it's near Nagoya, ~1.5–2 hours by shinkansen each way, tickets are timed and zoned, and it's a poor fit unless you really love the films.