A day out and about in Melbourne CBD in September

I'll be traveling to Melbourne in September and other than a mid-afternoon meeting will be in the CBD with not much to do between 11am and about 8pm on a Thursday.

I'll have a little luggage - a gym bag and a carry-on - and a little cash, but looking to do this on the cheap.

What's the best way to spend time but not money, with access to human necessities and somewhere to keep my bags safely?

I'd happily go to art galleries, museums and other cultural attractions, markets and other food places, I could use a gym if there's a good place for a single session, and even just sit in a comfortable place to read - all suggestions are welcome.

I'd avoid traveling outside of walking distance of the CBD if I can.