Airways Museum

Airways Museum
Street Address:
Wirraway Road, Essendon Airport
Postal Address:
Box 6, 20 English St, Essendon Airport, Victoria 3041, Australia
Phone: +61 (03) 9818 4950

If I may quote from their own site (as they say it much better than I could!):
The Airways Museum is an aviation museum, but with one difference - there are no aircraft! Instead, the Museum houses a collection of national importance that traces the development of Australia's civil aviation airways system through innovation and technical development from it's beginnings in the 1920s to today. The story is told through artefacts and photographs, and illustrates how Australia has often played a leading role internationally in aviation development.

It's not open very often so check times before you roll up.

You can get to their site here:
Airways Museum

Go to Australian Air Museums page from Airways Museum page
Go to Grubby Fingers Home from Aiways Museum page