You can probably get out to Canberra for a day or two while based in Sydney (It's a 3 hour drive,) if you so desire. Come and spend 5 minutes being underwhelmed by the NASA deep space tracking station's visitor centre.
I do recommend spending time somewhere other than Sydney/NSW though. There is a bad joke about how horrible life outside of Australia must be, because of all the tourists that come to Australia, never leave Sydney and then return home remarking how wonderful it is, even though Sydney is clearly the worst city in Australia. This is mostly unfair, however it is significantly different to the rest of the country, (akin to comparing New York with the rest of the USA.)