Most of what you come to Lübeck for sits on the egg-shaped Altstadt island. The Holstentor, the great brick churches, the Rathaus, the merchants' houses on Mengstraße and Königstraße, the medieval courtyards hidden behind unassuming alleyway entrances — all are within a thirty-minute walk of each other. The compactness is part of the pleasure: you can walk the entire historic city in a long morning.
Start with the Holstentor and the salt warehouses next to it, then cross into the Altstadt, climb St Petri for the panorama, walk through the Rathaus, visit St Marien, and finish at the cathedral at the southern tip of the island. Add the European Hansemuseum to learn how the Hanseatic League actually worked, and the St Annen Museum Quarter for the city's medieval art.