I am travelling to Australia for business in early August. I will be there for two weeks. I have a free weekend and can spend it in either Melbourne or Perth. I have heard such wonderful things about both cities, I am hoping some Australian natives or people familiar with these cities can help. Things that are important:

1) Which has better weather in August?
2) I will not have an automobile, so I will be travelling by taxi or rail to visit the area
3) I will be by myself, so I need things to do that do not require other people.
4) This is my first time to Australia

Thanks so much for any help you all can provide, I welcome all suggestions!