The Sonnenborgh is actually two museums in one: upstairs has an exhibit on the history of astronomy in an 1850 building that was once among the foremost astronomical research sites on earth. Below are the foundations of the much older city-wall bastions on which it was constructed.
Big redesign plans mean that by the time you read this, a new multilingual system using tablet-guides should have made the whole experience very interactive and thought-provoking. On certain days you can look through the ancient telescopes, whether at the sun (1pm to 5pm Sunday) or at the moon, stars and planets (April to September only). The latter is currently 8pm Friday and 7.30pm Saturday (€10), but check the website for updates and do prebook online.