Hamburger Sternwarte is Hamburg University's historic observatory, set in a park of protected neo-Baroque buildings in Bergedorf. The appeal is the combination of old astronomy instruments, telescope domes, and the slightly eccentric campus atmosphere of a scientific site that still feels apart from the city.
Public tours are the best way to see it properly, usually on Sundays or by arrangement. It is a trip out from central Hamburg, so check opening details before going.