Firstly, I highly recommend exploring French Island, which remains untouched by modern amenities such as electricity and water pipes. You can access the island by booking a bicycle in advance, then driving to Stony Point and catching a ferry. During my own visit, I even spotted a couple of koalas up close - they were running freely and I was only 50cm away!
More information can be found at https://www.westernportferries.com.au/ and https://www.visitvictoria.com/regions/phillip-island/see-and-do/tours/naturaliste-tours---from-phillip-island. Another must-see location is the Mornington Peninsula, where you can take a leisurely stroll along the famous Fort Nepean Walk and soak in the Peninsula hot springs. Market days fall on the weekends and can be found on Google Maps.
I would also suggest exploring Phillip Island, specifically Cape Woolamai and Churchill Island walks. Market days vary, so it's best to check on Google Maps for details.
VIEW IN GOOGLE MAPS Additionally, there are other places of interest in Melbourne's surrounding areas.
If you prefer natural scenery, horse riding and hiking, you may want to visit the Yarra Valley, Dandenong Mountains, Lakes Entrance, or Wilson's Prom (I'm looking forward to hiking the Mt Bishop Summit trail once it opens again). If you prefer the west side, I recommend checking out Daylesford, Hepburn Springs, Ballarat (known as the gold town), or the Great Ocean Road.
Example of a 7+ day itinery
28/12 : Melbourne CBD, city circle tram, St Kilda, Crown, SouthGate (French bistro)
29/12 : Box Hill central,lunch @ Yami Yami Korean Restaurant, Mount Dandenong, Sky High restaurant
30/12 : Doncastor - westfield shopping centre(Grant mall, it has nice food court), Dockland - Italian dinner
31/12 : Late breakfast, pick up vicky, go to Flinders st station to meet up my friends, dinner @ the pub, then wonder around Crown, return to the pub for dancing.
1/1: Late morning - visit Philip Island ;) saw little penguin running around. - Fish and chips, and late dinner @ Box Hill Chinese Restaurant - huge serve of porridge.
2/1: Early morning - Great Ocean Road (snack), China town for dinner, Lygon Street for 2nd dinner + dessert.
3/1: Big breakfast, Queen Victoria Market, Smith St, Bridge Road (lunch), Visit Windsor hotel[Victoria/Windsor/Executive Suites, Sofitel/Prestige suites, Sofitel Cafe La for dinner - very enjoyable
4/1: Souvenir hunting, Breakfast @ Box Hill, Doncaster Westfield Shopping centre, take train to CBD, Photo time, Lunch at South Gate - Italian eGusto, RipponLea Mansion/Garden, St Kilda - real fish and chips for dinner.