Look around the city, there are lots of options, there laneways with murals, shops, Chinatown for lunch, pub crawl, go to the sporting precinct, the Botanical Gardens, the Queen Victoria markets, museums, galleries.
Rydges is right by the airport I.e about 75 metres.
Otherwise you gave many hotels in Mascot that have airport shuttles for a fee. Mascot has a train station but the hotels are mainly around 300m or more from it.
If your Sunday flight is a similar time, perhaps stay in the CBD,or close to the cruise terminal, it makes it easy to drop your bags and to get around town on the Saturday. As you are in a hotel ( no ship delays), getting to the airport on Sunday would be less stressful.
I really think the officials stuffed it up with the start, first they call them back due to a jump start, then issue no penalty or tell of any decision made, all with a delay of 10 minutes.
Not sure what was happening. There was supposed to be a 5 second delay for the jump start, did they all jump the start?