Białystok is a manageable, walkable city — almost everything worth seeing sits within twenty minutes' walk of Kościuszko Square. The Branicki Palace and its gardens are the headline sight, followed by the Orthodox Cathedral, the Ludwik Zamenhof Centre, and the surviving traces of the city's Jewish heritage. The Podlaskie Museum holds a solid regional art collection in the old town hall on the square.
Set aside half a day for the palace and gardens and another half-day for the rest of the centre. The Bridges of Tatar villages and the Białowieża primaeval forest are the real reasons most travellers come to this corner of Poland — see Day Trips.