The Budapest History Museum occupies the rear wing of the Royal Palace; it's tucked behind a lovely courtyard and the entrance to the National Library. There's an extensive permanent exhibit dedicated to the history of Budapest that includes local archeological artifacts as old as 40,000 years on display. The Royal Palace as it exists today is not original: it has existed in many forms since the 13th century and has been repeatedly destroyed and then rebuilt over the years. The museum details these various incarnations, and on the underground levels there are some ruins and restored rooms, and a wonderful hidden chapel. The third floor is another highlight, with historic maps of battle plans and weapons used in the liberation from the Turks. There is also an outstanding collection of Roman and medieval-era pieces. You could spend days exploring this museum, depending on how deep your interest in Budapest runs. The courtyard garden and tower (accessible only through the museum) has amazing views, and is a great place to take a break.