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Its architecture is a stylistic potpourri reaching back to the 12th century. It is still the seat of the city administration and not a museum, so you can't have a look inside on your own. But there are guided tours every hour or so where the many historic rooms and the gallery of city leaders' portraits are explained (in German and possibly other languages).
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Christmas market
Or Marienkirche: the biggest one, a fine brick Gothic building near the Rathaus (city hall) at the centre of the Altstadt.
Dedicated to the brothers Thomas and Heinrich Mann, who spent their youth there. It contains many of their works. Closed until 2023.
Petrikirche
Its tower platform (which can be reached by an elevator) offers a great view over the city, and if weather conditions allow it you can even see Travemünde (17 km to the north-east).
A museum dedicated to all kinds of theatre puppets.