You don't need to eat in restaurants! Especially if it's Australia. There's more of a cafe culture - eat at lunchtime/in malls, snack in the evening.
I'm assuming you're coming here, but I think the same applies to most long distance destinations.
You could use the time to recharge with no obligations from anybody - no work or partner. Get up early, sit on the beach, watch the sun come up and breathe the ocean air. Visit Taronga Zoo, look at the amazing views over the harbour and see the native animals.
Tour the opera house, go paddleboarding, drive up the coast - the scenery is breathtaking.
There is so much you could do, that will stay with you, that doesn't need a friend or partner.
Don't stress about being on your own. Who cares? If you see somebody on their own on a plane or in a cafe do you think "you saddo?" or do you not even bother to wonder whey they are alone? They could be a business traveller, or somebody travelling with a large party who wanted to go off and explore. It doesn't matter.