Monte Igueldo closes the western end of La Concha bay, and from its summit you get the classic elevated view back over the city: the crescent of the bay, the old town with its terracotta rooftops, Monte Urgull with its white Christ statue, and the sea beyond. It is one of the great views in Spain.
The way up is by funicular — a steep, wonderful little cable railway that has been running since 1912. At the top there is a small vintage amusement park with a viewpoint tower. The rides are charmingly archaic, and the views from the tower are even better than from the funicular station. The walk down through the wooded western slopes of the hill, past the Miramar Palace, is a pleasant alternative to taking the funicular back down. Allow a couple of hours for the ascent, the views, and the walk back.