It will be freezing by the time july rolls around. Especially in the morning.
Public transport isn't too bad, so long as you avoid peak times!
Other items I suggest:
- Boat cruise on Melbourne River Cruises
- Bridge Road for shopping
- Brunswick Street for food
- If you can, take a drive east up to the Dandenong Ranges
- Instead of the Rialto, the Eureka tower is another option (it's taller)
- And for something indoors: Chadstone, Southland or Highpoint shopping centres