Poznań is Greater Poland's historic centre, where the legend of the two goats plays out at noon on the Old Market Town Hall. Ostrów Tumski, the cathedral island, is among the oldest seats of the Polish state. The city mixes a tight old town with a big international fair and a university crowd.
It sits roughly between Gdańsk and the west, so many travellers pass through as well as stay. Give the market square, the island, and a walk along the Warta a few hours at least.