The city centre, the waterfront, and the Magdalena Peninsula are all walkable if you don't mind hills. El Sardinero is about 3 km from the centre — easily reached on foot along the seafront promenade, or by city bus (lines 1, 2, 3, and 4 all stop there). Taxis are plentiful and cheap. There is no metro.
Renting a car is worthwhile if you plan to explore Cantabria: the caves at Altamira, the coast at Liébana, and the towns of Comillas are all within 90 minutes.