Central Luleå is compact and very walkable — most of the city-centre sights are within fifteen minutes on foot from the cathedral. The main exception is Gammelstad, which is about ten kilometres away and best reached by local bus (line 9 runs regularly from the central bus station). Teknikens Hus and the university are about three kilometres north and also served by local buses.
The city has a well-maintained network of cycle paths, and bicycles can be rented at the central station. In winter, many locals cycle year-round on studded tyres. Taxis are available and not outrageously expensive by Swedish standards. A car is useful if you want to explore the wider archipelago or drive the ice roads in winter, but not necessary for central sights.