Nice one. I haven't been to Apollo Bay but I'd imagine you'll probably spend a fair bit of time down at the beaches there - supposed to be quite good.
In terms of touristy stuff to do in Melbourne; I'd recommend hitching a ride on the City Circle Tram, which is a free hop-on hop-off service that does loops of the city. You get a good overview that way.
Stuff like Flinder's Street Station, Eureka Skydeck, Melbourne Museum, Scienceworks and Queen Victoria Market are good places to visit. If you can get down to the MCG on a day when the cricket isn't on, I'd recommend a tour and a visit to the Sports Museum. If you're into art, the National Gallery of Victoria is pretty good or a visit to A.C.M.I.
You can do wine tasting at some wineries in the Yarra Valley as well if that's something you're interested in.