US to Autralia people: me and my cousin

We will be there until march 20th(need to be home before 22nd)

Is it viable to do some things in sydney for 2-3 days then take a flight to melbourne for the rest of the trip?

What would you highly recommend doing in Melbourne other than bars or nightclubs?(we dont drink or party and we are in our early 20s)

Is there anything major i need to plan for ahead of time?

I just found out my passport is expired can i still get one in time?

(i read the faq but wanted more user input)