Wandering Bilbao's streets, you'll inevitably end up crossing Plaza Moyúa. Also known as Plaza Elíptica, due to its oblong shape, this main “square” is more than just a central crossroads, but a garden- and fountain-filled roundabout worth checking out and even stopping in (especially given its central area accessible to pedestrians).
Originally designed back in 1873, Plaza Moyúa sits in one of Bilbao's most exclusive neighborhoods, where it bisects the bustling shopping street Gran Vía. The plaza itself is dotted by various noteworthy buildings, such as the 20th-century Flemish-style Palacio Chávarri, the headquarters of the Civil Government since 1943, and the Hotel Carlton, the city's most famous hotel, which stands alone on its own spoke-like corner of the square.
The plaza is also a convenient location to catch the city's Metro – the third-busiest in Spain -- which rises out of Moyúa with its glass-domed entrance. Traveling underground, you can easily reach other parts of the city via two different lines.
You can reach Plaza Moyúa via Metro, of course, but also pretty easily by foot from most central locations. It is situated just a ten-minute walk from the Guggenheim – walking south on Alameda Recalde Zumarkalea – and a short jaunt from the nearby Bilbao Fine Arts Museum and Doña Casilda Iturrizar Park.