Metro
Busan's subway has four lines and covers most of the major sights. Line 1 (orange) runs north–south through the city centre and serves Jagalchi Market, the UN Cemetery area, and Nampodong. Line 2 (green) runs east–west and is the main tourist line: it connects Centum City, Haeundae, and Gwangalli Beach. A T-money card (the same card used in Seoul) works on all buses and subway lines.
Bus
Buses fill the gaps the metro misses. Haedong Yonggungsa Temple is most easily reached by bus 181 from Haeundae subway station. Gamcheon Culture Village is a short walk from Toseong station but some buses stop closer.
Taxi
Plentiful and cheap by European standards. Most drivers do not speak English, but the destination written in Korean on your phone is usually enough. Kakao Taxi (the Korean equivalent of Uber) works well and allows you to request in advance.
On foot
The city is hilly and sprawling — long-distance walking between districts is impractical. Within areas (Nampodong, Haeundae, Gwangalli) walking is fine. Wear good shoes; the slopes in Gamcheon and around the old port are steep.