Sydney has a lot of rainy days regardless of the time of year. Why not have some fun with that and sing in the rain? You can either sing in the rain while you're going to and from places, or you could take the opportunity to make some money.
Find a nice spot and just start singing in the rain. This is of course busking, so you'll need to make sure you have the relevant City of Sydney busking permits. When you do, you'll find you forget that it's raining and are just having some fun with it.
Singing in the rain can be a really fun way to pass the time and make money. The best spots to sing in the rain are on George Street or near a train station as there's a lot of foot traffic and you stand to make some good money.
Singing in the rain will help you turn a grey day into a fun day and that's got to be a great thing. It's also completely free and you can either do it by yourself or with friends.
There's loads of transport nearby so you can easily find a spot and if you find you want to move to a new location that's extremely easy to do.