Bunbury's best-known attraction is also its most unusual. Up to 90 bottlenose dolphins have made Koombana Bay their home, and they regularly come into the shallows to interact with people. The Dolphin Discovery Centre on the foreshore is the hub for this: you can wade in and hope for an encounter, or join a boat cruise out into the bay.
The old city has some worthwhile heritage buildings. St Patrick's Cathedral has an unusual history — built in 1921, elevated to cathedral status by Pope Pius XII in 1954, then damaged by a tornado in 2005 and rebuilt. The Old Bunbury Railway Station, a brick building dating from 1905, now serves as the bus interchange and visitor centre.
For nature, the Leschenault Estuary lies just north of the city — a 25 km lagoon with ancient mangroves, up to 62 waterbird species, and boardwalk access through the mangrove colony. South of Bunbury, the Tuart Forest preserves the largest remaining stand of pure tuart woodland in the world, with a scenic drive and spotlighting trail for nocturnal possums.