Pack some food and drinks for the afternoon hike. There is no supermarket, cafe or lunch spot nearby.
While you can use your stroller for the morning hike in Bilbao, you have to switch to a baby carrier to access the island of San Juan de Gaztelugatxe for the coastline views. The island is connected to the mainland by a man-made stone bridge and has 241 steps to reach the top.
You can do a city stroll any day of the week, but on Mondays the Guggenheim Museum is closed.