Well, Rosie...There is one bar in the CBD where I would take you, called e55. It is under-ground, the music is always wicked, drinks are cheap and considering its position in the city it remains pretty much absent of morons and hipsters. Great place for a drink on weekdays especially, when the DJ need not play to the crowd and you can find a seat. Brilliant decor...good atmosphere.
Perhaps a visit to the Brunswick Green would also be on the agenda, a traditional pub in the laid back, rough around the edges, still cheap-ish suburb of Brunswick. Wonderful rear courtyard and decent staff.
My garden would be a better stop all round, with a few of my freak friends in attendance, Oscar demanding attention at your lower paws, my regular feast cooked as my savage queen and I host, and enjoy connecting quality, colourful characters. (much to the chagrin of my Lady, I ALWAYS prefer to host people at our place, where I can cook, choose the music, and most importantly, include Oscar in the festivities)
As for a trip outside the city...perhaps Hampton beach would be pleasant for a swim. The great ocean road has numerous natural pleasures as well as the ocean. Or perhaps a camping trip to Lake Eildon.
And what if I headed your way???
PSSSS...I forgot the Botanical Gardens in the city...
So...when does your plane land at Tullamarine????