The west coast of Australia enjoys a mild climate throughout the year, so don't hesitate to leave Perth to explore the beautiful region of the south-west. Unless you're travelling with the family, I would not advise you to go directly to Bunbury, but further south toward Dunsborough, Grace Town, Margaret River or even Busselton with its famous pier.
In fact, Bunbury seemed dull: it is not very beautiful, with an industrial and commercial centre and a rather busy port. Along the port, I particularly remember the enormous houses with stunning architecture: the sign of a certain economic wealth. Like any industrial city, there is nothing particularly picturesque to see there. However, there is a nice area in Bunbury, which is worth a stop especially if you have children - Koombana Bay. This isthmus, between the port and the Leschenault marshes, possesses a family beach with a playground and picnic area, and especially the Dolphin Discovery Centre, which is definitely the number one visitor attraction in Bunbury! A place that will delight all ages. On this stretch of land, I was happy to escape a little from the urban area. You can observe the flora and fauna during a stroll along Mangrove Walk, for example.