If you're in Bendigo, this is pretty much a 'must' in terms of seeing a whole different side of the town. Their Chinese heritage goes back all the way to mining days and this museum has some really fascinating tidbits of information about the way things began and developed over time amongst the Chinese. It also has this incredibly hugely massively long Chinese dragon, I think it's like the largest in the Southern Hemisphere or something like that.
Now this isn't really a 'kid friendly' museum - infact it'd be dead boring for most kids because there's nothing you're allowed to touch, so leave them at home. On the positive side, entry is cheap and it doesn't seem busy.
The Chinese gardens are really nice too, a relaxing place to sit aside for a while and with some nice views over Bendigo.