First time visiting Australia with mom

Hi all! I'm visiting Sydney at the end of November with my mom for a wedding. After the wedding, we'll have 3 days to explore Sydney, followed by 5 more days to visit another city. Would you recommend any other places for that second leg? Melbourne or the Great Barrier Reef or any other areas that are must explore?

A bit of context: we're not comfortable driving on the opposite side of the road, so we're planning to rely on tour buses and public transit for everything. Any suggestions or tips would be greatly appreciated!