G'day Dayers, depending on your interests (bush Vs beach, etc...) there are some cracking wanders up Mt Albert, Mt Victoria and out the back of the Moorina / Weldborough / Pyengana / Goshen areas for an easy day trip fron "Snellens" (sorry, local humour).
Others that come to mind, Mt Paris Dam (disused) and the upper Cascade valley and Mt William National Park.
Joe has covered some of the others I've mooched about on too.
There was a group of shack owners out near Binnalong that organised treks up the beaches and scrub from Ansons towards Musselroe Bay during their holidays, but I don't know of any formal process or association out there which you could tap into.
Harridge Falls is a great place to get into, and a relatively easy place to access from the Tasman Hwy. For me, it's all about fly fishing but sometimes I have an official "photographer" in tow to capture the scenery.
Good luck with it.