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Here are maps as a guide to some roads that are less travelled, being perhaps more suited to Enfields but also more interesting than highway riding.
Back roads to Beechworth - from Beechworth a number of roads open up follow links below.  Beechworth has a number of pubs for accommodation the Old Priory offers the cheapest accommodation at $50 a night for dormitory type beds.  Riding the extra 45km to Albury may be in order for cheaper accommodation at the Railway Hotel at $40 a night.
Back roads to Bruthen - via Moe for petrol, from Bruthen a number of roads open up follow links below.  Bruthen has a motorcycle friendly pub, The Bruthen Hotel, that you can stay at as well, last time I stayed there (2012) they charged $30 a night.  You could ride the extra 66km to Orbost where there are two hotels that are reasonably priced.
Other roads to consider:

Beechwoth and beyond

Bruthen and beyond