Bendigo Art Gallery was founded all the way back in 1887, but its collection is anything but dated. Sure, the gallery features works from as far back as the 1850s and gold rush, but in recent years it's also developed something of a reputation for hosting cutting edge fashion exhibitions on Mary Quant, Balenciaga, and contemporary Indigenous designers.
While in the area, it's also worth checking out the Golden Dragon Museum (it's just a quick walk from the gallery through Rosalind Park).