This link lists the centre points of Australia, the States and Territories:
http://www.ga.gov.au/scientific-topics/national-location-information/dimensions/centre-of-australia-states-territories#heading-8
The centre of the ACT is: S 35° 29.400 E 149° 00.084, but you won't find this cache there, instead you will find it almost there at: S 35° 30.025 E 149° 03.089
This spot has a lovely view though.