One of my favourite rivers. It's in south-eastern Australia S36.123821 E149.486795 and it's a legendary wild brown trout stream. People from, say, the USA would look at it and call it a creek rather than a river.
On both occasions I've visited I've seen a platypus playing in the water, at two different locations. The name of the river is said to derive from early white settlers believing that the local wombats were badgers. On my last visit I sat near the bank, watching a platypus play as the sun set. After a while a large wombat emerged from his burrow, about 20 metres away, watched me for a bit, and proceeded to graze. The funny thing is, he was faintly striped and looked a bit badger-like.
There is a wonderful account of holidaying and fishing on the Badja river in Douglas Stewart's fine book "The Seven Rivers". Also John Hedge's Trout Fishing - A Season on the Monaro has some good anecdotes. The old fishing lodge they stayed at, now abandoned, is close to the GPS location above, near the road bridge. The nearest town of significance is Cooma.