I’m so envious, I love Melbourne!!
Definitely go to the Penguin Parade at Phillip Island. I’d recommend doing the Guided Tour there as one of the rangers is your guide and you learn so much more. The whole experience is incredible (I’ve been a couple of times as it appears that I’m now addicted to little penguins).
If you’re a wildlife lover (assume so if you’re going to see the penguins), I’d recommend a trip to Healesville Sanctuary. Incredible place. And it’s 1 hour from Melbourne in the Yarra Valley so combines perfectly with doing some wine tasting in the Yarra. I’d recommend Yering Station for wine tasting and lunch.
I did a walking coffee tour (half a day) in Melbourne which I really enjoyed. We went to some great places that I would never discovered on my own (and that I’ve gone back to on subsequent visits) and it was a good way of getting my bearings as well as meeting a few people and getting more tips (I was on a tour with an Aussie couple who were just back the GOR where I was going the following day). Incredible coffee of course.
I really like St Kilda. It’s easy to hop on a tram there and back for lunch/dinner/the day. I liked it so much that I chose to stay there for a few days in an AirBNB on a later visit. If you like gemstone jewellery, there’s a fabulous shop/gallery called Made in Earth that is worth a visit.
I used to live in HK and had a close friend from HK who moved back to Melbourne so I used to visit quite a lot. Quite frankly, I’ve never forgiven her for then moving to Sydney as I much prefer Melbourne. 😩
If you fancy an overnight (or two) away, you can get flights to Tasmania from Melbourne. It’s only a short hop (just over 1 hour). You could fly over to Devonport (tiny airport), hire a car and drive to Cradle Mountain (90 mins from Devonport) and stay there for a day or two. I stayed in these log cabins and had pademelons bouncing up and down on my balcony and roof every night 😍:
https://www.cradlehighlander.com.au
And it’s walking distance from the cabins to fascinating Devils at Cradle which is a Tasmanian devil sanctuary. I went one evening to a devils with wine tour where we tasted wine and cheese and then were shown round the sanctuary whilst drinking wine and getting to mean baby devils. Absolute bliss!
https://devilsatcradle.com/