Though the Bilbao "Metropoli" ranges for miles up and down the Ría de Bilbao (the estuary of the Nervión), the part of the city you will be exploring comprises under 3 km (1.8 mi), from the downstream Palacio de Euskalduna to the upstream Mercado de la Ribera. The subway can be handy for a quick shot from one end of town to the other, but is not a necessity for getting around unless you need to make an opera curtain or soccer kickoff.
A 20-minute excursion on Norman Foster's designer subway will get you close to the beach at Getxo, while a train ride from the narrow-gauge Atxuri station through the Urdaibai natural park reaches Mundaka and Bermeo in under an hour.
If you begin from Bilbao and circle out along the coast of Vizcaya province and into the Basque hills, the beach resort of San Sebastián is less than an hour northeast while Pamplona is an hour southeast, close to the French border. Vitoria and La Rioja Alavesa are less than an hour inland from Bilbao.