If you don't know much about the history of Budapest, you can amply remedy that in this four-floor museum in Buda Castle
Better Known as the Castle Museum
Commonly known simply as the Castle Museum due to its location in Buda Castle, this exploration of the history of the Budapest area is spread over four floors and includes pieces dating back a whopping 40,000 years (such as a cave bear skull and stone tools). Much of the collection and recreations focus on the Middle Ages and the history of the castle itself (as of this writing, the section on Budapest as of 1868 was still under construction). In the meantime, the halls and passageways of the museum are as much of interest as the displays themselves. Like most other Budapest museums, it's closed Mondays; also, November through February it closes early, at 16:00, rather than the usual 10:00-18:00.