Collectors Corner has taken over Missing Link and is actually on the same street a few doors down. It intermittently has some good stuff.
Record Paradise in St Kilda is worth a look, as are the assorted Dixons (the one opposite Yong Green Food in Fitzroy yields some good things from time to time). Heartland near Vic Market is good for metal and has some nice second had stuff in periodically.
the best two in my opinion are Vicious Sloth (more price-y high end stuff. all their records are immaculate condition) and Licorice Pie in Prahran.
There are a bunch of others around the city that throw up stuff from time to time. There is a leaflet with all the small record shops that you can pick up and work through
If you get the chance to do the Great Ocean Road or get into the country side then do it, but there's lots of cool tourist-y stuff within the city. The Gaol is meant to be very good (although i've not been there yet). The Eureka Tower is quite cool if you're comfortable with heights. If the weather is nice then the Botanic Gardens are great to mooch around in - they have an open air cinema there over christmas/summertime too.
The Astor cinema in St Kilda is an awesome art deco cinema that shows old double bills and recent movies and is well worth a visit.
Gig wise, Useless Children and White Walls play the Tote on 22 December. they are both great. Cut Sick playing the Gassometer on Christmas Eve and if you are around over New Years, Limpwrist are playing.